The first colonists that came over from England in 1733 were (naturally) Anglicans. They founded the first church in the colony of Georgia, and named Christ Church.
In its early days, John Wesley was the presbyter from 1737 to 1738, and then returned to England and began a movement that would become the Methodist Church. He was succeeded as presbyter by the great evangelist, Charles Whitfield.
The southeast Trustee lot of Derby Ward, to the east of Johnson Square, was given to the congregation to erect an edifice. The cornerstone of the first building was laid in 1740, and it was completed ten years later. It burned down in the great fire of 1796.
The second building was consecrated in 1815, but razed to the ground in 1837. The current building you see today began in 1838 and was consecrated in 1840.
After the American Revolution, the congregation did what many Anglican churches did. To remove any English ties, they became Episcopalian.