Even if you had such a fantasy strong material to build it from, a rigid ring doesn't have a stable orbit. Once the tiniest thing knocks it slightly off center, like a single meteor impact, or even the gravity of a passing meteor that doesn't even hit it, the ring would quickly shift further and further off center until one side hits the planet. The orbit isn't self-correcting once you make the object rigid. Quite the opposite - whichever side is closer to the planet gets a stronger pull that pulls it even closer to the planet.

If you wonder why that doesn't happen to individual orbiting satellites, that's because individual orbiting objects that are knocked closer the the planet take on an eccentric elliptical orbit shape which is still stable. But a rigid ring is still stuck in a circle shape even when the "proper" orbit that would remain stable should be an eccentric ellipse.

This raises an interesting question of whether a ringworld that was flexible such that it could be deformed into any ellipse could keep a stable orbit. It still probably couldn't because the same energy orbit that was a circle, when it deforms into an ellipse, ends up being an ellipse with a larger circumference than it had as a circle - so it would have to be both infinitely flexible and infinitely stretchy. That's why a field of rocks and dust can form a stable orbit ring shape (they can form a shape that is infinitely flexible and stretchy since they're not really one joined object.) While a single-object ring really can't.