1883, from French rastaquouère, rastacouère (19c.) "social intruder, upstart" (especially one of exaggerated manners and dress, from a Mediterranean or South American country), thus "dashing but untrustworthy foreigner" [OED].
Short form rasta is attested from 1905. According to French sources, the word is from South American Spanish rastacuero "upstart," from arrastrar "to drag, pull, tow, trail along the ground" + cuero "leather." Arrastrar is said to be from Spanish rastro "rake," from Latin rastrum (see raster), while cuero is from Latin corium (see corium).