The Light Blues will be hopeful of sealing their progression in the competition having already overcome the Diamonds this season.
The sides met in the Scottish League One in August and Rangers ran out emphatic winners with a 6-0 victory at the Excelsior Stadium.
Ally McCoist's men will be looking for a repeat of that result when they take on Airdrie at Ibrox in the cup, before again playing host to the Lanarkshire outfit in league competition the following weekend.
Scottish Cup third-round draw in full:
Forfar Athletic v East Fife, Culter v Berwick Rangers, Elgin City v Dunfermline Athletic, Stranraer v Auchinleck Talbot, Alloa Athletic v Inverurie Loco Works, Ayr United v Queen's Park or Preston Athletic, Rangers v Airdrieonians, Dumbarton v Cowdenbeath, Arbroath v Brechin City, Stenhousemuir v Buckie Thistle or Annan Athletic, Edinburgh City or Fraserburgh v Montrose, Turriff United v Stirling Albion or Whitehill Welfare, East Stirlingshire v Raith Rovers, Albion Rovers v Deveronvale or Linlithgow Rose, Clyde v Brora Rangers or Cove Rangers, Queen of the South v Hamilton.
Ties to be played on the weekend of November 2.