Fraser joined Celtic when he was eight progressing through the youth ranks signing a three year professional contract in the summer of 2010. Whilst a member of Celtic's under-19 squad, he was called up to the first team for a friendly match against Athletic Bilbao on 26 March 2011. He made his debut the following season, on 3 November 2011, in a 3-1 win against Rennes in the Europa League. He came on as a substitute at half time and played in the centre of defence. Fraser made his first start for Celtic in an SPL match against Inverness Caledonian Thistle on 9th February 2013.