Liam played underage football with Arklow Town before joining UCD's U19 squad for the 2015 and 2016 seasons. In 2016 he was involved with the senior team during their pre-season friendlies and he made his senior debut in a 4-1 win over Cabinteely at Belfield on 8 July 2016. He scored his first senior goal in a 1-1 draw away to Athlone that September and finished the season with two goals from 13 league appearances.

He moved to Shamrock Rovers for the 2020 season. After over 50 appearances for Shamrock Rovers, Scales signed a four-year contract with Scottish club Celtic in August 2021. On 23 September 2021, he made his debut for Celtic in a 3–0 win over Raith Rovers in the Scottish League Cup at Celtic Park.