Not very big! It would just have to be natural. Not made by man! And it wouldn’t have to be there for very long either. Just long enough for it to be in orbit.
The astronomical community doesn’t have a definition for moon other than it has to be a natural object. Thus captured asteroids can be moons. It’s even possible for a moon to have a moon!
Mars has two moons, neither of which are large enough to be round. Objects in space get round due to their own gravity. The first image above is Deimos and the second is Phobos, the Martian Moons. Deimos (top) is the smallest. It has a mean radius of 3.9 miles.