Dundee born goalkeeper Peter Robertson began his career with local junior club Lochee United in 1926 before joining Scottish League Dundee in 1927. He then signed for Second Division club Charlton Athletic in August 1929, making his Football League debut against Cardiff City at the end of the same month, missing only one game for The Valiants in his debut season and being ever present in 1930-31. However his place came under competition from Gerry Keizer and Alex Wright and in December 1933 he transferred to Crystal Palace after 126 appearances for The Addicks.
The move to Palace did not prove a success, Robertson made 4 first team appearances in January and February of 1934, and returned to his hometown to join Dundee United after the end of the season. He had a single season at Tannadice making 37 appearances before joining Brechin City in the summer of 1935, and he moved to Arbroath in 1936, replacing Dave Cummings after he left The Red Lichties to join Middlesbrough. He remained at Arbroath until signing for Rochdale in May 1939, however having played in the first three fixtures of the 1939-40 season, the season was abandoned due to the outbreak of the Second World War, which effectively ended his career.