Is it socially appropriate to ring up a professor whom you have corresponded with briefly by email?
I don't see any problems for you to call him.

If you want answers quick, this is the best way to achieve it. If you feel a bit uncomfortable calling him, then I suggest that you "ping" him with re-sending your last mail or that you ask him if he can reply from the previous message.

Teachers at my university, some have their phone number (Both private and work, though private is not mandatory) listed at the university website so that students can reach them outside of working hours if it's urgent.

So having students call them is nothing new and shouldn't be a problem.