Originally signed by the Arizona Diamondbacks organization, Stockman was a Texas LeagueAll-Star in 2003, while working as a starting pitcher for the El Paso Diablos. He signed with the Braves as a six-year minor league free agent in 2006, and earned a midseason promotion to the majors. His contract was purchased from the Richmond Braves on June 14, 2008 in place of RHP Chris Reitsma, who was placed on the 15-day disabled list. He made his debut the next day. On 16 May 2008 Stockman was called up to the major leagues and pitched 1 scoreless inning of relief against Oakland on 17 May, which included his first two career strikeouts (which were Mark Loretta and Josh Beckett.)
He was released on 15 March 2009 due to injuries. He has not played baseball since, and has retired.