The Shakers will continue their 2018/19 FA Cup journey with a home tie against Luton Town.
Nathan Jones' side currently sit 5th in the Sky Bet League One table with eight wins from their opening seventeen games.
The Hatters gained promotion after finishing second in League Two last season and secured their progress to the second round by beating Wycombe Wanderers 2-0.
Details for the game, such as a confirmed date and ticket prices will be confirmed in due course.
The full second round draw is:
Guiseley v Fleetwood Town
Bury v Luton Town
Wrexham v Newport County
Tranmere or Oxford City v Southport
Southend or Crawley v Barnsley
Shrewsbury or Salford City v Scuthorpe Utd
Solihull Moors v Blackpool
Chesterfield or Billericay v Grimsby
Peterborough Utd v Aldershot or Bradford
Swindon Town v Woking
Maidstone Utd v Hampton & Rich or Oldham
Lincoln City v Carlisle
Morecambe or Halifax v AFC Wimbledon
Plymouth Argyle v Oxford Utd or Forest Green
Barnet or Bristol Rovers v Stockport
Rochdale v Portsmouth
Walsall v Sunderland
Accrington Stanley v Ebbsfleet or Cheltenham
Mansfield or Charlton v Chorley or Doncaster
Sutton or Slough v Gillingham or Hartlepool