Jensen began his career in music cutting records for Colpix, for whom he recorded his first single in 1959. He graduated from high school in Fort Lauderdale in 1960 and then recorded with Kapp Records and its subsidiary, Leader Records. In 1962 he moved on to Hickory Records, where he began recording many numbers by Nashville staff songwriters such as Boudleaux and Felice Bryant, Roy Orbison, Joe Melson, and John D. Loudermilk.
In 1962 he recorded “Torture”, which Loudermilk had originally written for The Everly Brothers. The song became a hit, reaching #20 on the Billboard Hot 100, and after its success the Everly Brothers decided to record it as well. The song proved to be Jensen’s only hit, though he recorded at least 32 songs over the course of his career. Reissues of his catalog were released to LP by Bear Family Records in 1979 and to CD by Sparkletone Records in 1995.