Wanderers will face League Two side Barrow AFC at home in the last 32 of the Papa Johns Trophy.
Friday night’s draw means a reunion for Whites’ boss Ian Evatt with his former club.
Evatt – and most of his current backroom staff – guided the Bluebirds to promotion back to the EFL in 2020 after a 48-year absence prior to moving to take charge of Wanderers.
The fixture at the University of Bolton Stadium is due to be played in the week commencing 21 November with further details to follow in due course.