Rapp is best known for originating the role of Mark Cohen in the hit musical Rent, a role he also played in the movie version of the musical. In addition to Rent, Rapp's Broadway credits include The Little Prince and the Aviator, Precious Sons, Six Degrees of Separation, You're a Good Man, Charlie Brown and If/Then. His screen credits include Chris Columbus’ film version of Rent as well as Star Trek: Discovery, Adventures in Babysitting, School Ties, Dazed and Confused, Six Degrees of Separation, Man of the Century, Road Trip, A Beautiful Mind and more. In 2000, he released his debut album Look Around.