Rapp was selected out of the University of Southern Mississippi by the San Francisco Giants in the 15th round of the 1989 amateur draft.  He made his Major League debut with the club in 1992, posting an 0-2 record. 

Left unprotected in the 1992 expansion draft, Rapp went to the Marlins with the 10th pick. In Florida's inaugural 1993 campaign, Rapp joined the rotation in July. He would post a 4-6 record with a 4.02 ERA in 94 innings.

In 1994, Rapp's wins went up while his ERA went down, as he posted a 7-8 record with a 3.85 ERA in 133.1 innings pitched.

1995 was Rapp's best season with the Marlins, as he posted a career best (and NL fifth best) in wins, going 14-7.  He also posted a career best in ERA, with 3.44.

Over five seasons with the Fish, Rapp started 115 of 117 games, accumulating a 37-43 record with a 4.18 ERA.

Rapp was traded back to the Giants in mid-1997 for Bobby Rector and Brandon Leese. He later went on to play one season each with the Kansas City Royals, the Boston Red Sox, the Baltimore Orioles and the Anaheim Angels.