After being given a bye at the first round stage of the competition, Phil Parkinson's men now face a trip to Pools' Victoria Park in around a month's time.
The draw is an exact repeat of two years ago when City were pitted away to Hartlepool in the second round after being handed a bye in the first round.
On that occasion a single Leon McSweeney goal edged the tie in the hosts' favour.
Parkinson's side are scheduled to make the journey north to Hartlepool the week commencing 8 October 2012.
Admission details for this tie will be announced in due course.