David Murray began his playing career with Glasgow Rangers, though he failed to break through with the Scottish giants and joined Everton of the English First Division in 1903. He made two first team appearances for the Merseysiders before crossing the city to sign for Second Division Liverpool in May 1904. He played in twelve games as the Reds won the Second Division title in 1904/05.

Murray had three games in the top flight before signing for Leeds City for £150 in December 1905 as the Peacocks sought to strengthen their defence. He was pitched straight into action, featuring in ten games on the bounce during which he was asked to fill both full-back positions. He was also nominated as City's penalty taker and opened his account for the Peacocks from the spot in a 4-1 defeat of Leicester Fosse on 20 January.

Murray missed three games in February, but ended his first season for City with 3 goals from 23 appearances, having established himself as a mainstay of the side.

Murray took over as City captain after John George lost his place early in the 1906/07 campaign, and he continued to give consistent displays, though he missed large chunks of the season between December and April through injury.

Murray was a regular choice throughout 1907/08, now being partnered by Harry Kay, and missed just four games.

The Scot was unavailable for the start of the 1908/09 season with a cartilage injury and had a barren time, not appearing in the first-team at all until 23 January. He was only selected twice more after the game and in 1909 he signed for Mexborough Town. He later played for Burslem Port Vale.

Murray joined the Army after the onset of World War I and died, aged just 32, in Loos, France, on 6 October 1915.