This name began to be used in America in the 1970s, possibly inspired by Princess Aisha of Jordan (1968-), the daughter of King Hussein and his British-born wife. It received a boost in popularity after Stevie Wonder used it for his first daughter in 1975.
The name was brought to public attention by Samuel A. Taylor's play Sabrina Fair (1953) and the movie adaptation Sabrina that followed it the next year. This is also the name of a comic book character, Sabrina the Teenage Witch, first introduced 1962 and with television adaptations in 1970-1974 and 1996-2003, both causing minor jumps in popularity. Another jump occurred in 1976, when it was used for a main character on the television series Charlie's Angels.