After backing up All-American Jim Davidson as a sophomore, Current became a starter as a junior in 1965. Prior to his senior year, he was named a team co-captain, along with defensive back John Fill and center Ray Pryor.
The American Football League’s Denver Broncos selected current in the third round of the 1967 AFL/NFL common draft. He was traded to the AFL's Miami Dolphins where he played for two games before being traded back to the Broncos. He played with the AFL Broncos from 1967 through 1969 and for the NFL Broncos from 1970 through 1975. He was picked up by the NFL Tampa Bay Buccaneers in the 1976 veteran allocation draft, and returned to the NFL Dolphins from 1977 through 1979.