I am Nigerian and have never been to Tbilisi, Georgia. I will be entering the country with a UK visa, so I booked a one-way ticket.
Do I have to book a round-trip ticket since I have not been there before?
As per Timatic, the database used by airlines:
Warning: - Visitors not holding return/onward tickets could be refused entry.
While I myself have only ever been asked for a return ticket once (which was not in Georgia), it is possible citizens of poorer countries will be subject to more scrutiny.
Thus, you should at least buy a refundable ticket, bring the confirmation to the border, and cancel it once in Georgia