Wrexham have been drawn at home to Conference North side Solihull Moors in the FA Trophy second round.
Andy Morrell's side, who beat Rushall Olympic 5-0 in the first round, will host Solihull Moors on 15 December.
Merthyr Town face a trip to Blue Square Bet Premier side Dartford if they overcome Tonbridge Angels.
The two sides meet on Tuesday after Saturday's first round tie at Penydarren Park was postponed.
FA Trophy Second Round Draw
Dartford v Merthyr Town or Tonbridge Angels
Stockport County v Southport
Maidenhead United or Sutton United v Oxford City or Bishop's Stortford
King's Lynn Town v AFC Telford United
Bromley or Boreham Wood v Kidderminster Harriers
Forest Green Rovers v Gainsborough Trinity
Tamworth v Corby Town
Cambridge United v Gateshead
Woking v Welling United
Wrexham v Solihull Moors
Chesham United v Hyde or Barrow
FC Halifax Town v Maidstone United
Hereford United v Hampton & Richmond Borough or Chelmsford City
Grimsby Town or Buxton v Braintree Town or Havant & Waterlooville
Boston United or Skelmersdale United v Guiseley
Mansfield Town or Matlock Town v Dorchester Town or Luton Town
(Ties to take place over weekend of Saturday 15 December 2012)