It was on The Family's debut album in about 1982. This was one of Prince's little spin off groups, which included Susannah Melvoin, sister of Wendy who played guitar with the Revolution. It was actually a bloke (called St Paul!) who sang it on the album.
squiggle is correct. While Prince certainly wrote the song, the first recording of it was by The Family. In fact, all The Family's material was written by Prince, but the man himself was not a member of the band. Some members of the band later joined Prince's backing group, The Revolution.