Davidson was selected in the fourth round of the 1961 NFL draft by the New York Giants, but was traded in training camp to the Green Bay Packers.
As a rookie, he played mostly special teams for the Packers in 1961, who beat the Giants 37–0 in the championship game, the first of five NFL titles for head coach Vince Lombardi. During training camp in 1962, Davidson was traded to the Washington Redskins for a fifth round draft choice.