No Prince wasn't a JW during his childhood like the Jacksons (for example) were.
Here's a quote from the Wikipedia entry on Prince:
In 1997, Prince approached funk bassist Larry Graham, one of his childhood idols, with questions about his [Graham's] Jehovah's Witness faith. In a later interview, Graham stated that Prince was in need of Biblical answers and advice and that Graham was glad to answer. Prince apparently became very interested in the religion: around this time he began censoring some of his more provocative song lyrics in concerts, as well as editing various religious references in his songs that he had come to believe were Biblically inaccurate. [citation needed] He was baptized by Jehovah's Witnesses in 2001, marking his formal conversion to the faith. It was also at this time that he also released the album The Rainbow Children, which relied heavily upon Jehovah's Witness religious themes.
The insertion of Graham's was mine.