Abercromby came through the youth ranks at St. Mirren and signed a full professional contract in 1975. A year later he experienced his first involvement with the first team squad when Sir Alex Ferguson called him into the squad to tour the West Indies.
On 29 October 1986, Abercromby was sent off for three red card offences, one for foul play and two counts of dissent during a match against against Motherwell at Love Street. As a result, he was banned for twelve matches. He won the 1987 Scottish Cup when St. Mirren beat Dundee United 1–0 in the final. He was transferred to Partick Thistle in 1988.