Wrexham will face either Torquay United or Chesham United in the FA Trophy fourth round.
Gary Mills' Wrexham reached the fourth round with a 4-2 win at Tranmere Rovers on Saturday.
National League rivals Torquay United beat Southern League Premier side Chesham 2-0 in a third round replay on Tuesday.
Kevin Nicholson's Torquay will host the Dragons on Saturday, 16 January at Plainmoor.
.Wrexham beat Torquay United in last season's FA Trophy semi-finals and won 1-0 in the league at Plainmoor on 5 December.