The two sides drew 1-1 at the Crown Oil Arena on Saturday and will now meet again at St. James' Park on Tuesday, 14th January (kick-off 7.45pm GMT).
The match will not be televised after the BBC opted for Tottenham Hotspur's replay with Middlesbrough while BT Sport chose to show the all-Premier League affair between Manchester United and Wolves.
Miguel Almirón gave United a first-half lead in the first tie at Rochdale, but Aaron Wilbraham equalised in the 79th minute to force a replay.
The winners will face League One Oxford United at home in the fourth round.
Ticket details are here.