c.1300, "a quick, light blow, stroke," also "a fart" (late 15c.), native or borrowed from a Scandinavian source (cf. Danish rap, Swedish rapp "light blow"); either way probably of imitative origin (cf. slap, clap).
Slang meaning "rebuke, blame, responsibility" is from 1777; specific meaning "criminal indictment" (cf. rap sheet, 1960) is from 1903. To beat the rap is from 1927. Meaning "music with improvised words" first in New York City slang, 1979 (see rap (v.2)).