O.C.G.A.§ 19-3-30 (c):  The license shall be directed to the Governor or any former Governor of this state, any judge, including judges of state and federal courts of record in this state, city recorder, magistrate, minister, or other person of any religious society or sect authorized by the rules of such society to perform the marriage ceremony; such license shall authorize the marriage of the persons therein named and require the Governor or any former Governor of this state, judge, city recorder, magistrate, minister, or other authorized person to return the license to the judge of the probate court with the certificate thereon as to the fact and date of marriage within 30 days after the date of the marriage. The license with the return thereon shall be recorded by the judge in a book kept by such judge for that purpose.

Georgia, like most states, defers to the rules and polity of the “religious society or sect” when determining who may officiate at a ceremony.