City have won once at Cheltenham, while the Robins have won twice on home ground in the three league match there. The last time the two teams played was at the KC Stadium in August, when City came from behind to claim a 3-3 draw.
Managerless Cheltenham are currently 15th in Division Three, and were beaten 4-0 by Mansfield today.
Last season City went out in the First Round after defeat to Macclesfield, while Cheltenham lost in the Third Round at Sheffield United following victories against Yeovil and Oldham.
The full draw is as follows:
Lincoln v Brighton
Peterborough v Hereford
Oldham v Carlisle
Cheltenham v Hull City
Yeovil v Wrexham
Macclesfield v Boston United
Grays or Margate v Aldershot
Scarborough v Doncaster Rovers
Barnet v Stalybridge Celtic
Blackpool v Boreham Wood
Wycombe v Swindon
Lancaster City v Cambridge United
East Thurrock or Woking v Histon
Bournemouth v Bristol Rovers
Eastbourne or Stevenage v Stockport County
Grantham v Leyton Orient
Thurrock v Luton
Northampton v Plymouth
Tranmere v Chesterfield
Hornchurch v Darlington
Scunthorpe v Shrewsbury
Torquay v Burton
Accrington Stanley v Huddersfield
Grimsby Town v QPR
Notts County v Shildon
Brentford v Farsley Celtic or Gainsborough
Kidderminster v Northwich or Halifax
Southend v Mangotsfield or Canvey Island
York City v Barnsley
Port Vale v Ford United
Mansfield Town v Bishop Stortford
Sheffield Wednesday v Salisbury City
Farnborough v Weston Super Mare
Chester City v Exeter City or Gravesend
Telford or Tamworth v Crawley Town
Colchester v Oxford United
Bradford Park Avenue v Bristol City
Bury v Rochdale
Swansea v Rushden & Diamonds
Hartlepool v Bromsgrove or Whitby