Barney was selected by the Detroit Lions in the second round, 34th overall pick, of the 1967 NFL Draft. As a rookie in 1967, Barney appeared in all 14 games as a starting cornerback and led the NFL with 10 interceptions, 232 interception return yards and three interceptions returned for touchdowns. After an injury to Pat Studstill, Barney also took over as the Lions' punter, punting 47 times for an average of 37.4 yards in 1967. On September 17, 1967, in the first quarter of his first NFL game, Barney intercepted the first pass thrown in his direction by Bart Starr and returned it 24 yards for a touchdown. In the final game of his rookie season, Barney intercepted three passes within ten minutes and returned one 71 yards for a touchdown. At the end of the 1967 season, he was selected by the Associated Press as the NFL Defensive Rookie of the Year.