Beasley began his professional career with Birmingham, but left to join Torquay United in 1935 without making the first team. He scored on his league debut on 18 January 1936, a 2–1 win at home to Watford, Torquay's other goal coming from Fred Beedall.
He played in the following two games, a 2–0 defeat away to Bristol City and a 3–1 defeat at home to Millwall in which Beasley scored Torquay's goal. Despite scoring he was replaced by Wally Hunt for the next game. He made one further appearance, on 14 April 1936 in a 3–0 defeat away to Bristol Rovers before leaving for non-league Worcester City. He later played for Halesowen Town.