Tinsley was drafted by the Chicago Cardinals as the 12th overall pick in the 1937 NFL Draft. He played for the Cardinals for three years: in 1937, 1938 and 1940. As a rookie in 1937, Tinsley set an NFL record with 675 receiving yards. He also ranked among the NFL's 1937 leaders in several categories, including 36 receptions (second in the NFL), 675 receiving yards (first in the NFL), 677 total yards from scrimmage (second in the NFL), five receiving touchdowns (second in the NFL), 18.8 yards per reception (first in the NFL) and 61.4 receiving yards per game (first in the NFL). At the end of the 1937 season, Tinsley was selected as a first-team All-NFL player by the United Press, the NFL, "New York Daily News", and "Collyers Eye" magazine.