The Potters will host the tie at Clayton Wood on Tuesday 8th March (kick off 1.00pm).
City have been awaiting news of an opponent for the game since progressing through the group stages of the competition back in December.
A Joselu hat-trick, along with strikes from Oliver Shenton and Mame Diouf, secured a 5-2 victory over Wigan Athletic just before Christmas in a result that followed on from September's 5-0 win against Wrexham and the 1-1 draw at Port Vale in October.
Group C winners Stoke will face a County side with a 100% record from their three Group D games whilst the other Semi-Final in the Northern Cup sees Burnley travelling to either Hartlepool United or holders Middlesbrough.
The Potters were inaugural winners of the Central League Cup competition back in the 1996/97 season.