The League One leaders, winners of the cup in 1913 and 1957, will play the Angus side away on Saturday, January 9, for the second year in a row.
Dick Campbell’s team are currently one tier and two places above Falkirk, sitting second bottom of the Scottish Championship with five points from nine games.
Falkirk aren’t far behind them, being top of League One with 21 points from 10 games.
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The two teams have only encountered each other twice before in the Scottish Cup, both those meetings being in January this year.
Their initial fourth-round match at Arbroath’s Gayfield Park on Saturday, January 18, ended goalless, taking the tie to a replay at the Falkirk Stadium on Tuesday, January 28.
That rematch was won 2-0 by the Bairns, thanks to goals by Declan McManus on 47 minutes and Conor Sammon on 66.
Overall, according to soccerbase.com, Falkirk have got the better of the sides’ 43 meetings since 1937, winning 24, twice as many as Arbroath, with seven draws.
The other ties drawn tonight, December 28, ahead of Dundonald Bluebell’s game at home to Queen’s Park, being broadcast live on BBC Scotland, were Kelty Hearts v Stranraer, Keith v Clyde, Dumbarton v Huntly or Cumbernauld Colts, Stirling Albion v Raith Rovers, Buckie Thistle v Inverness Caledonian Thistle, Forfar Athletic v Linlithgow Rose, Camelon or Brora Rangers v Heart of Midlothian, Dundee v Bonnyrigg Rose Athletic or Bo’ness United, Formartine United v Annan Athletic, Nairn County v Montrose, Elgin City v Ayr United, East Fife v Tranent Juniors, Alloa Athletic v Cove Rangers, Airdrieonians v Edinburgh City, Peterhead v Stenhousemuir, Fraserburgh v Banks o’ Dee, Greenock Morton v Dunfermline Athletic, Partick Thistle v Cowdenbeath and Queen’s Park v Queen of the South.