As an anti-social person, do you think that I wouldn't fit for a Public Relations Officer job position?

Of course as you should be social in order to acheive your targets and get closer to the others.

Before answering your question i would like to say, someone has rightly said " not knowing is a source of learning". if you are anti social then how would you learn and develop yourself? you will need to go to a place where you can meet people who are social and the best way to meet those people is PRO. though it would be difficult for a month or so but you will feel comfortable and developing yourself after that. when i was first appointed as a CSR in call center, i was very shy and my friends were laughing at me when i used to eat in cafeteria because i didn't even know how to eat in such environments but i kept on walking and now i am a manager in word's first class IT company at pakistan. it depends on you that how you present yourself.