Dickey was drafted by the Texas Rangers in the first round (18th overall) of the 1996 Major League Baseball Draft and later debuted with the Rangers in 2001. Dickey was a member of the 1996 US Olympic Baseball team that won a bronze medal in Atlanta. Dickey started two games, recording wins in both.

From 2007-2010, Dickey played minor league baseball for the Brewers, Mariners, Twins, and Mets. He became a knuckleball pitcher in 2006. In 2010, the Mets purchased Dickey's minor league contract and he debuted back in the majors on May 19. In 2012 Dickey was selected to his first career All-Star Game.