The round one draw, which took place this Tuesday morning, saw Phil Parkinson's men given a trip to York's Bootham Crescent as their first confirmed match of the forthcoming 2015/2016 campaign.
City's full League 1 fixture list for the new season will be announced at 9:00am on Wednesday (17 June 2015).
The Bantams' match at York is scheduled to take place the w/c 10th August - meaning it will be City's second match of the season after their season opener in the league.
Ticket details for this tie will be revealed in due course.
Under the guidance of former Scunthorpe United boss Russ Wilcox, York finished 18th in League 2 last season.
Coming just under a week after the club's appearance in the Capital One Cup Final, City's previous visit to Bootham Crescent ended in a 2-0 win for Phil Parkinson's men back in March 2013 thanks to goals from James Hanson and Garry Thompson.
The full draw for the first round of the Capital One Cup can be seen below: