Impactor Threat
- Instead of asteroids, you probably want a comet, also known as "dirty snowballs". Consists mainly of ice and sand, mud, small rocks etc. making them perfect for shiny, sparkly rings.
--> Advantage: Because of the tail, it can be seen from much greater distance (and probably during daylight also) than an asteroid (that doesn't reflect light most of the time, let alone producing a tail).
A comet would just not be that much of a threat, though. They would probably disintegrate/vaporize when entering the atmosphere (but will certainly cause some effect; see comment by @Gilgamesh).
Asteroids would be a real threat (but ruled out). It seems like a good motivator though having a deadly threat...
--> You can have an hybrid as well, like with a rocky core and an icy crust. Still needs a good explanation why the mages know the internal composition of that object or care about it and why they conclude that this is a cataclysmic event. A comet looks so pretty...
--> Even when using a "not direct impact course" (or even a hyperbolical course, making the comet leaving the system again for forever), a good motivation for mages might be "superstition", "bad omen" or the "assumed danger of the unknown celestial body", "end of the world" etc. (although it wouldn't be one; well, depends on the circumstances really when/if impacting)
Creating Rings
Shoving some big rock into the Roche limit is not the only way to create planetary rings.
Rings can also form when the solar system and the host planet form. This can lead to stable rings because the system "grew up together".
--> This would miss the effect of creating them, though. The people would be totally used to having them all their life, rather. Particles entering the atmosphere will (or plausibly can) be much lower in numbers.
- You can have any debris forming the rings (also think many many small "satellites") orbiting a planet in basically any stable orbit higher than the planet's atmosphere. This needs their angle of attack, mass and speed to be "right".
--> Could be adjusted to match the explosion of the comet. This would again need some kind or orbit or tangential course, not a direct impact course. Forming of the rings would not be instantaneous, but arguably a lot (huge lot) faster and more plausible than "Roche grinding". Think maybe several years (or as you see fit. Also within a day would easily be "plausible" I think -> geostationary orbit then (or close to)). But because of the explosive nature, those rings would probably not last for too long (at least not for forever), because being spread thin over time and eventually dissolve.
Concerning Roche / The Roche limit seems to be popular these days ;)
Roche grinding needs a really slow approaching on an descending orbit. The Roche limit will not disintegrate everything that crosses it auto-magically! Especially not if crossing in a straight line (collision course). Roche grinding and collision course are pretty much mutual exclusive.
Roche grinding is awfully slow, especially if the object has much material to be grinded to tiny dust speckles (unless you pull something from the sleeve). Think in terms of thousands or millions of years for a "simple" asteroid or comet that was "stopped".
A moon takes more like a billion years (more rather than less) to be finished for good, and would break up into several large pieces multiple times during that process.
--> Meaning, the image in the sky would be most likely this new moon/asteroid, accompanying the planet for many generations/forever in human-terms, with an ever so slightly growing tail of debris forming the final state of the rings eventually (the asteroid/moon would also sweep the particles away constantly). Larger pieces of the moon will impact the planet on several occasions probably. Causing devastating effects at least locally (think of an radius of about 100km to 1000km and more, depending on size/mass and speed).
--> A moon is most likely so heavy that the gravity of the planet will have it pulled-in to impact long before it is grinded away. Let alone the increased tides (tsunamis) and other catastrophies that would be caused by that big/heavy object that close (near the Roche limit). A moon so close is like being able to be touched by hand, would appear much bigger than the sun in the sky, would be visible at the brightest daylight and cast a big shadow onto earth. Our moon for example is like 300,000km away from earth, not like <10,000km. Imagine our moon would be 30x larger. Also that moon has to be pretty damn fast on its orbit to maintain staying at the Roche limit and not crashing into the planet. Inducing winds in the atmosphere constantly, probably stronger than any hurricane we know. Living on the planet surface would pretty much be impossible.
--> A moon (not even a small one, I'd say) is not feasible at all for your purpose of "no harm to the planet" (Technically an asteroid orbiting earth is also considered a "moon", but I mean it in terms of size here. Moon being multiple times larger than an "average" asteroid).
- Roche limit cannot be computed for real objects of actual mass, material composition etc. It is a theoretical value, based on heavily simplifying assumptions. A mage knowing the correct limit to park an asteroid there, will cause some very serious frowning on the reader's side, I guess (or they don't care). This has never even been computed on earth once, because it is virtually impossible. Ok, they are mages, but still... strange. This needs a good explanation to work.
- Most people never heard of the Roche limit. You could not just throw in that term and everybody goes "ahaa, good thing they cared about that [in a fantasy world] acknowledging nod".
--> I deem it more plausible that the mages just let the asteroid/comet instantaneously disintegrate by magic power (can still cost them something), still a safe distance away before any harm can reach the planet, and only dust clouds, icy particles, etc. remain that sling around the planet to form the beautiful rings more or less instantaneously (or as you see fit) and everybody rejoices over it in awe.
--> If sticking with the Roche grinding, keep in mind: When entering the atmosphere, atmospheric drag would inevitably cause particles to be decelerated and to heat up because of the friction, causing either "micro-meteors/shooting stars" (glowing and burn up in the atmosphere) or even some that are able to survive (depending on material mostly) and impact the planet (named "meteorites" then). This would happen probably at a very high rate during the whole time. Having either very visible or almost no visible effect, depending on size, material composition and again mass, speed, angle (and maybe more factors, like day/night time, gravity of the planet, composition of the atmosphere, weather conditions etc.).
Also under special conditions, but possible, would be the creation of effects like the aurora borealis at the poles, when those particles enter atmosphere.
Fantasy vs. Physics
Bluntly speaking, if I may: I'd find it super odd, reading about mages (probably having all the power I can think of), but then they act totally bound to the laws of physics. Why didn't they summon a dragon and send him there to clear out the asteroid/comet instead of computing a Roche limit?
--> Maybe this is your intention. But I think, actually you are searching for an explanation to have rings on the planet and something that ties the mages together (not a rug ;)). Hope I could provide you with some ideas.