Is it socially appropriate to ring up a professor whom you have corresponded with briefly by email? A couple of weeks back I sent an email to a professor in a University in my home country with whom I have never known on any personal or professional level. My intention was to seek potential collaborations with him as a recent graduate with a BSc should I return home. 

He did replied and to which I responded. One of his question to me was whether I am happy to collaborate without being paid to which I replied, "Yes, I am happy but I am only able to work on any project outside of standard office hours due to foreseeable industry commitment".

Since then, I have not received any replies. 

Would it be appropriate for me to ring him up?
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.