People have thought about similar projects, though perhaps for reasons of engineering practicality there hasn't been much effort directed at canals for the purpose of transport.
The problem is that the Gulf of Aquaba is part of a long rift system that runs along the Israel-Jordan border, including other notable water features such as the Dead Sea, the Sea of Galilee and the River of Jordan.
Rift valleys are inconvenient, because they don't necessarily have flat bottoms, they won't necessarily contain watercourses that lead out to the sea, and they often have large mountainous or at least hilly regions to either side of them, and the Jordan rift valley is no exception.
With a bit of careful inspection of openstreetmap and the use of this handy tool, I was able to sketch out a very rough route following what looks like the lowest mountain passes available:
and the elevation profile of the route:
This should show you two very important things.
The canal is long. Longer than the Panama canal which is a mere 82km, and longer even than the Suez canal which is over 190km. At 280km, this canal would be a major feat of engineering even in the absense of the high, steep sides of the rift structure.
the terrain is hilly. The route of the Suez canal is flat and low lying over its entire length. The Panama canal route is less convenient, and involves raising ships up to 25m above sea level and making a 95m deep cutting, but that's nothing compared to this thing where the high points are nearly 500m above sea level.
Your canal would be one of the largest and most formidable civil engineering projects ever undertaken, even without the issue of being in one of the most politically unstable parts of the world that's also quite geologically unstable... very undesirable given how many large and complex locks would be needed to help raise boats and water high enough! And that's without even taking into account how massively hot and dry that part of the world is, and the need to continuously pump water up from the sea to counteract evaporation.
L. Dutch suggested that you could use nukes to dig your canal... indeed you'd probably have to. And as luck would have it, someone else also had this idea, and wrote about it! Use of Nuclear Explosives for Excavation of Sea-Level Canal Across the Negev Desert.
It takes an initially similar route to the one I proposed above, but uses a more northerly pass through the hills so that it lies entirely with Israel's borders. The route is similar in length to mine, but passes through more hilly terrain.
The author of the report assumes:
- 30 miles of conventional digging techniques
- an average depth of cut of 750 ft
- channel width of 1000 ft (equivalent to the widest sections of the Suez canal today)
- 2 megaton devices buried at 1300 ft
- 4 devices per mile
- 130 miles of excavation using nuclear explosives
That's 520 nuclear warheads with a total yield of 1.04 gigatonnes.
The nuking would have been done in "virtually unpopulated desert wasteland", which the author assumed would have made it OK. The amount of long lasting radioactive contamination this would have generated would have been breathtaking. This proposal would have been made right at the beginning of the Project Plowshare and Nuclear Explosions for the National Economy era, before the severity of nuclear contamination became obvious to everyone. The Soviet Taiga tests in 1971 more or less drew a line under the idea of digging canals with nuclear blasts.
If you'd like a slightly more plausible way to transport cargo along a similar route, consider the Negev desert railway which would link the Israeli Mediterranean coast with Eilat, which lies next to Aqaba at the top end of the Red Sea.
The route from Eilat to Dimona would likely follow a similar route to the nuclear canal idea. The plan has been put on hold indefinitely, at least in part because it presents an economic threat to Egypt and the whole region is politically fragile enough without giving it a good kick.
If you were open to trains and alternative routes, then why not go from Basra on the Persian Gulf, through Iraq and Syria and up to Turkey? The Berlin to Baghdad Railway was a thing, once upon a time, and trains from Basra to Baghdad still run from time to time...