Arthur was born December 26, 1888 in Waycross, Georgia, the son of John Spencer and Emma Victoria (née Cason) Moore. Arthur was of Irish ancestry. His great grandfather came to North Carolina and his grandfather moved to Georgia.
Arthur's grandfather later died in the Battle of Gaines' Mill in 1862.\r\nArthur married Martha "Mattie" T. McDonald April 26, 1906. They had children William Harry, Wilbur Wardlaw, Alice Evelyn Means, Arthur James Jr., and Dorothy Emma. Mattie died in 1964.