I'm not sure about rabbits and broken nails, but something like this happened to my dog a while back. She had jumped off of the couch bed that was out, and her nail got stuck in the metal and pretty much almost ripper her nail off. Hers was pulled out by the "root" i guess you would call it. Hanging sideways. I took her into the vet and she had to have it removed in surgery. But that was only because the WHOLE nail was torn out partially.
Is his nail just broken in half, or is it the whole thing that is at a 90 degree angle? If its just broken in half, I would think it should be fine as long as you have controlled the bleeding and keep it clean, as with any small wound. But if the entire nail is coming off, I'd suggest going to the vet. Good luck, and let us know how it goes.
Sorry if my advice is not helpful, I haven't owned a rabbit since I was young. :/