Plowman originated in the Macedon Ranges from Sacred Heart College, Kyneton. In 2011 and 2012 he played in the TAC Cup for the Calder Cannons, playing primarily as a tall defender. He was drafted to the AFL by Greater Western Sydney with the third overall selection in the 2012 national draft.
He made his AFL debut in the opening round of the 2013 season. He played eighteen games for Greater Western Sydney over the first two years of his career, winning a regular place in the team in the latter part of 2014. An elbow injury limited him to only two senior games in 2015.
In October 2015, Plowman and three other Giants teammates (Jed Lamb, Andrew Phillips and Liam Sumner) were traded to the Carlton Football Club.