Edinburgh born outside right Jimmy Davidson played for Leith Athletic in 1891 before signing for Glasgow Celtic in 1892, making his debut for The Bhoys, scoring in a 2-2 draw at Rangers that September. Celtic won the Scottish League Championship for the first time in their history in his debut season, and his debut goal proved its importance as Celtic won the title by a single point from Rangers, with Davidson contributing 7 goals to the campaign. However he lost his place the following season to Johnny Madden and spent two seasons on the fringes at Parkhead before leaving to join First Division Burnley in July 1895 after having scored 10 goals in 22 appearances for Celtic.
He made his Football League debut at Wolverhampton Wanderers that September and scored twice in 20 appearances for The Clarets, spending the spring of 1897 on loan at Lincoln City where he scored once in 9 matches. He then joined Southern League Tottenham Hotspur in the summer of 1897, spending a season with Spurs scoring 5 goals in 17 appearances, which was followed by a move to Brighton United in the summer of 1898, before Davidson returned to Turf Moor to re-join Burnley in the spring of 1900. Although he scored the only goal of the match on his (second) debut in a win over Sheffield United in April, he couldn’t help save The Clarets from relegation, and he spent two more seasons with the club in the Second Division, scoring 5 goals in 47 further appearances in his second spell before retiring from football in 1902.