Birds are relatively small compared to other theropods. For example, the Moa, the largest known bird, is 12ft from head to toe, which is the same height as a T. rex at the hip. Two problems that I think might prevent large birds would be the fact that birds' legs are not under the pelvis, and that birds have long, thin, flexible necks. So, would it be plausible for a bird to lose these traits and other traits keeping them small, allowing them to become similar in size to T. rex or other large theropods?
You're essentially asking for birds, which already came from the theropod dinosaurs and suffered heavy alterations to become lighter and more adapted for flight, to essentially re-evolve the traits they lost in order to grow. You're also asking for them to grow to the size of a T-rex when their ancestors were much smaller. Can they do it? Likely. T-rex came from a group of relatively small theropods, so with the right pressures to loose the ability to fly and grow bigger, they could likely return to a more landbound lifestyle, maybe even grow to those sizes. Is it likely in the world we know? No. Flying is an incredibly useful ability, which nowadays grants birds incredible advantage over other animals regarding their ability to move over long distances, explore certain niches with little competition other than other birds (and certain bats) and, for the past over 65 million years they've shown time and time again how useful flight can be. In addition, unless every creature is enormous, meaning carnivores too will have to grow larger, being relatively small is a good strategy, as you'll require much less nutrition than a creature 10 times your size, and is also the reason many birds survived the KT-extinction event.
So summing up: could they? Yes. They already came from theropods and animals like T-rex evolved from much smaller theropods, and animals re-evolving traits is far from unheard of. Would it be plausible for them to loose several adaptations and give up on the niches they already occupy to become once again landbound predators? Highly unlikely, as birds already existed during the Dinosaur era and still exist to this day, showing how advantageous their overall adaptations were from their survival (nowadays some suspect it was because of competition with birds that some pterosaurs had to grow bigger, as they were outperformed by the birds in the niche of small aerial predators).
Sure, why not? But rather than focusing on a t-rex-style predatory super-bird, which would be limited by the maximum size and abundance of its prey due to its obligate carnivorous lifestyle, your best bet, IMHO, would be some alternate/future evolution relative/descendant of the Hoatzin: the last surviving member of an order of birds which recent genetic studies have now shown branched off in its own direction more than 64 million years ago, literally as the ashes were settling shortly after the extinction event which wiped out the non-avian dinosaurs. But the reason I'm nominating them isn't for this reason, or the finger claws possessed by juvenile Hoatzins. it's because they're the only birds to have ever evolved a digestive system which utilizes bacterial fermentation to break down the vegetable material they consume, in the same manner as cattle and other mammalian ruminants do.
In the place of the mammalian ruminants' rumen (a specialized stomach for bacterial fermentation), in a case of parallel evolution, the hoatzin has evolved an unusually large crop instead, folded in two chambers, along with a large, multi-chambered lower esophagus. Its stomach chamber and gizzard are much smaller than in other birds. Their crop is so large as to displace the flight muscles and keel of the sternum, much to the detriment of their flight capacity. And the fossilized remains of an extinct species of Hoatzin has been found in Namibia, some 18 million years ago, proving that indicating that, in the African-South American interchange which facilitated the colonization of South America by new world monkeys, rodents, bats and other species, at least a few Hoatzins went the other way and successfully (albeit briefly) colonized Africa too (along with at least one species of Phorusrhacid/'terror bird'). As such, full flightlessness seems like an extremely likely evolutionary path for the Hoatzins to take.
So, how's about this for a alternate evolutionary scenario; over in Africa, as the climate gets increasingly arid, and the mangroves and rainforests begin to be replaced by savannah, instead of simply dying out as they did IOTL, some of these African Namibiavis Hoatzins manage to cling on by abandoning their arboreal lifestyle and adopting a more terrestrial lifestyle instead; rapidly losing their flight ability in the process, and becoming fully terrestrial. Their unique pseudo-ruminant digestive system would be far more efficient than, and provide them with a tremendous evolutionary advantage over, any other avian browsers and grazers (and potentially even mammalian ruminants), easily enabling them to outcompete contemporary ostriches, and far outgrow them as well.
And without the limitation to their maximum size imposed upon them by retaining their vestigial flight ability, combined with their far more efficient digestive systems granting them access to more nutrition than any competitors, and with the considerable evolutionary pressures placed upon them by African predators increaasing the evolutionary pressures towards gigantism, these African hoatzins rapidly grow to quite easily become far larger than any other ratites; large enough to realistically rival the mass and height of the largest ruminants, the giraffes, and feasibly, even some of the dinosaurs of old.
Studies of mummified hadrosaur remains indicate that they also possessed enlarged crops, most closely resembling those of Hoatzins- implying that hadrosaurs, and perhaps all ornithopods, which were the most successful group of dinosaurian herbivores in the Cretaceous and wiped out at their apex by the K/T extinction event, may also have evolved an extremely similar digestive system via convergent evolution. And this also implies that, theoretically, the Opisthocomidae family already has a near-identical digestive tract to that of a clade of dinosaurs which includes members which were longer, taller and heavier than the largest tyrannosaurs.
The original purpose of these Hoatzins' finger claws, for climbing, would have long been rendered redundant by this stage. But perhaps these African Megahoatzins still re-evolve arms, and refine their finger claws, in an evolutionary development paralleling those of the gigantoraptors, ground sloths and calicotheres when they all took the same evolutionary path? Equipped with increasingly large and developed claws, they could use them to strip leaves, tear off branches, and as potent and formidable defensive weapons against any predators who attempt to attack them or their nesting sites.
Or alternatively, these finger claws could evolve into psuedo-hooves (since re-evolving extra digits rarely happens, if ever), with a sub-order evolving to become semi-quadrupedal as an adaptation to support their increasing bulk and shifting to ground-feeding grazing, just like the hadrosaurs did; with this semi-quadrupedal stance also enabling these African Meganamibavis to become larger and heavier still, conceivably rivaling the size of the largest ornithopods. What do you reckon; does it sound feasible enough?
Theoretically, yes- given the right set of conditions, the history of evolution in vertebrates shows us time and again that species trend toward larger body sizes over time unless evolutionary pressure from environment or competing organisms keeps them restricted in size. Consider that the moment the non-avian dinosaurs disappeared, mammals began to explosively evolve and grow to fill those empty niches- from shrew to badger size to wolf sized within the first 500,000 years - which is remarkably fast but just goes to show how dominant the dinosaurs were over these large-bodied niches.
Consider also that mammals in a scant 65 million years went from burrowing animals the size of a squirrel to blue whales, elephants, giraffes and we humans and imagine what birds could do in another 100 million years. The dinosaurs themselves started out small and grew to massive sauropods by the late Jurassic, about 100 million years after the first small dinosaurs skittered around in the mid-Triassic. They too evolved after a mass extinction event.
The main obstacle to birds evolving into huge T. Rex sized brutes is that the dominant terrestrial predator and herbivore niches that they would likely evolve to occupy are currently filled by mammals- and ground-running birds are rare and must remain light and fast enough to run away from big cats and other mammalian predators- the birds after all have lost the advantages the non-avian dinosaurs had: big powerful heads filled with sharp teeth, clawed forelimbs, thick scaly skin instead of feathers over delicate chicken-line skin (contrary to recent trends, skin impressions show that the likes of T. rex and Carnotaurus were covered in scales, not feathers, and some small theropods had feathers and scales simultaneously), bulkier, more powerful legs and necks, and thick, muscular tails - these traits would make a bird a lot scarier for a cheetah or lion to try to take on as that weaponry could easily kill the cat or injure it which no predator wants - injured predators starve to death.
Point is, in order for birds to grow to these immense sizes and take up major ground-based super predator roles T. Rex and Allosaurus once took up….there has to first be a massive extinction event that kills off all the big mammals but for some reason the survival conditions favor fast-growing, egg-laying ground-running birds. IF humans and all mammalian predators - especially all cats of all sizes - were to become extinct and a few bands of birds - let’s say secretary birds, or even a few thousand cassowaries - survivded and faced zero competition their size or bigger, and they eventually evolved into predators….sure…with millions of years it could happen. It would HELP if there were an evolutionary arms race between predator and prey as we saw with the dinosaurs - prey got huge and predators grew to keep up - so there would have to be birds that became quadrupeds (4-legged), grew thick, stout legs and… well, probably they’d end up looking a little like sauropods, which may sound silly but again, recall that the likes of Brachiosaurus evolved from small bipeds way back in the Triassic- and the body plan of Triassic early dinosaurs was not that dissimilar from birds apart from birds losing the teeth, tail and two of their fingers fusing together)…
Given that, and no mammalian pressure, if the only remaining mammals were rat sized or smaller, it is certainly possible. One catch though is that historically, lost features do not tend to re-evolve once lost, so things like teeth or clawed hands might never appear again. Then again, millions of years make a lot of things possible - you are the direct descendant -literally - of a small fuzzy rodent-looking creature no bigger than a rat which cowered in burrows as the dinosaurs shook the ground overhead - and now here you are, a primate with self-awareness, a big brain and using this insane invention of ours - the internet - to communicate with symbols (letters and words) on a device that amounts to an electronic brain that we developed - from basically a rat to that in 65 million years - think what 65 million years could do for birds.
No, because theropods use their legs and wing/hands to push up while birds can only us their legs. If the bird's wings get bigger to lift a bigger bird the legs will need to get bigger to push the bigger bird into the air. Theropods avoid that by pushing up with the winds and legs. Like bats.