Davidson attended Baylor University, and played professionally for the NFL's Baltimore Colts (1954, 1957), and the AFL's Dallas Texans (1960–1962) and Oakland Raiders (1962–1968).

Davidson has the record for the lowest career completion percentage in NFL history, minimum 1500 passing attempts, at 43.9%.

By the time Davidson returned to the Colts for the 1957 NFL Season, John Unitas was the team's starting quarterback.

After the 1962 season opener, he was traded to the Oakland Raiders for the first overall selection in the 1963 American Football League draft.

The high moments of his career were being selected to the American Football League All-Star Game twice: in 1961 and in 1963.