The first round draw, conducted by FA Cup winners Paul Ince and David James, saw City pitted against Accrington for the second time this season in a cup competition.
Stuart McCall's men have, of course, already played Accrington once before in the EFL Cup first round at the Wham Stadium back in August.
Accrington are currently positioned seventh in the League Two following a 2-1 home win over Blackpool at the weekend.
First round ties in this season's Emirates FA Cup are scheduled to take place over the weekend of the 5/6 November 2016.
Ticket details for the Accrington home tie at the Northern Commercials Stadium will be confirmed in due course.