The draw was broadcast live on Sky Sports ahead of tonight's Championship game between Plymouth and Watford, which saw City draw away.
Match dates and ticket details will be announced in due course, but the Bantams will have to make the difficult journey to Edgeley Park.
Stockport currently sit fourth in League One.
The competition, previously known as the Bristol Street Motors Trophy, was renamed the Virtu Trophy effective immediately Thursday night.
Vertu Motors, a group that currently operates under the trading names of three automotive retail brands, including Bristol Street Motors, announced last month that it would combine the brands into one under the name Vertu.