Graham was born in Fayetteville, North Carolina. He played in the minor leagues for three years before joining the Giants on May 23, 1905. On June 29, the Giants were the visiting team against the Brooklyn Dodgers, then known as the Superbas. For the bottom of the eighth inning, Graham was sent in to play right field, replacing George Browne. In the top of the ninth inning, Graham was on deck (scheduled to be the next batter) when the Giants made their third and final out. He played the bottom of the ninth in right field but never came to bat, and that game turned out to be his only appearance in the major leagues.