 On November 17, 1992 during the 1992 Major League Expansion Draft held for the newly minted Florida Marlins and Colorado Rockies, Rapp was selected in the first round with the tenth overall pick by the Marlins.During the Marlins' first season in 1993, Rapp went 4–6 with a 4.02 ERA in 94 innings.During the strike shortened 1994 season, Rapp compiled a record of 7–8 with a 3.85 ERA, two complete games and his first career shutout.