He currently plays for Brora Rangers, wearing the number 14 shirt. He plays primarily as a Defender.

His most recent move was a from Clachnacuddin to Brora Rangers on 2014-01-24.

Throughout the Scottish League Cup 2025-2026, C. Williamson featured in 4 matches, averaging 0 tackles, 0 interceptions, and 0 clearances per game, while blocking 0 shots per game.