Arthur was born December 26, 1888, in Waycross, Georgia, the son of John Spencer and Emma Victoria (née Cason) Moore.
They had children William Harry, Wilbur Wardlaw, Alice Evelyn Means, Arthur James Jr., and Dorothy Emma.
Arthur experienced a "drastic" conversion to Christ in his twenty-first year and began to preach at once.
Moore was appointed to the Travis Park Methodist Church in San Antonio, Texas, serving there until 1926.
Dr. Arthur James Moore was elected and consecrated to the episcopacy of the Methodist Episcopal Church, South at the 1930 General Conference of that denomination.
Bishop Moore was assigned responsibility for all missionary activities of the MECS in China, Japan, Czechoslovakia, Belgium, Belgian Congo, Poland and Korea, until 1940.
In 1940 he was assigned the Atlanta episcopal area of the (newly reunited) Methodist Church.
Bishop Moore also served as president of Wesleyan College in Macon, Georgia, in 1941, and as chairman of the board.