Rangers, who crashed out of the Scottish Communities League Cup to Irn-Bru First Division Falkirk earlier this season, will travel to Second Division title challengers Abroath.
Holders Celtic face a trip to Peterhead, who are currently ninth in Scotland's bottom tier and managed by ex-Hoops defender Jim McInally.
Danny Lennon's St Mirren face a home tie against last season's relegation rivals, Hamilton Accies.
Motherwell have come out favourably, netting a Fir Park fixture against the winners of Saturday's replay between Third Division pair Queen's Park and Elgin while Kilmarnock face a potentially tricky trip to Dundee.
Partick Thistle, who were held to a shock 1-1 draw by Junior outfit Culter on Saturday, will face Queen of the South at Firhill if they can see off Andy Gibson's side in a replay, while West Region Juniors Auchinleck Talbot have a plum tie at troubled SPL club Hearts.
First Division rivals Morton and Raith Rovers face off at Stark's Park.
Meanwhile, SFA chief executive Stewart Regan will bid to secure some weekend fixtures when he negotiates Scotland's World Cup 2014 qualifying schedule.
Regan will meet counterparts from Scotland's opponents – Croatia, Serbia, Belgium, Macedonia and Wales – in Brussels tomorrow.
Scottish Cup fourth round draw:
Ross County v Stenhousemuir
Livingston v Ayr/Montrose
Raith v Morton
Hearts v Auchinleck Talbot
Cowdenbeath v Hibernian
St Johnstone v Brechin
Stranraer/Forfar v Aberdeen
Culter/Partick v Queen of South
Inverness v Dunfermline
Falkirk v East Fife
Motherwell v Elgin/Queen's Park
Arbroath v Rangers
Peterhead v Celtic
Airdrie Utd v Dundee Utd
Dundee v Kilmarnock
St Mirren v Hamilton
Ties to be played January 7-8