Carlton has joined the Shakers following his release from Carlisle and will aim to reignite his career at Gigg Lane.
He will face stiff competition for a place as Andy Bishop, Andy Morrell and fellow new recruit Ryan Lowe are also jostling for position.
Carlton said: "Anyone in the league would be happy to have four strikers like this.
"It will be good competition for next season. It can only make players better and make the team better."