Cranksets are typically sold with both arms, not just one of them, so the exercise of finding just a right arm that is compatible is mostly academic (the only case I can think of that's somewhat reasonable is a parts bin at a bike co-op or shop which has one, but this is still unlikely). You're more likely to find the whole crankset instead, in which case there isn't really a reason to not install both of them.
That being said, on a square taper bottom bracket, you can install different square taper crank arms on the left and right (different sizes, different makes, etc). You can mix hollowtech 2 crankarms on the left and right as well. So on, so forth -- the compatibility is determined by what type of crankarm you're running.
If you have an autoshop nearby or a bike shop, you can also try to helicoil the crankset. This puts a new set of threads on for the pedal.
Also, note that if you don't have a crank puller, you're going to have to borrow one or likely go into a shop unless the crank is self extracting.