 After high school, Rapp attended the University of Southern Mississippi.He was drafted by the San Francisco Giants in the 15th round of the 1989 amateur draft.Rapp's career through the Giants' minor league system included stops at Pocatello, Idaho, Clinton, Iowa, San Jose, California, Shreveport, Louisiana, and Phoenix, Arizona before getting called up to the big leagues by the Giants in 1992 at the age of 24.