Holders St Johnstone have been drawn away to Kelty Hearts or Montrose within the Scottish Cup fourth spherical.
Celtic, who’ve gained the competitors a file 40 instances, are away to Alloa Athletic.
Rangers, who final gained the trophy in 2009, will welcome League 2 Stirling Albion to Ibrox.
Ayrshire junior aspect Auchinleck Talbot are rewarded for his or her win over Hamilton Academical with a house draw in opposition to Hearts.
North Superleague outfit Banks O’Dee, who beat League 1 East Fife within the third spherical, have a house tie in opposition to Championship aspect Raith Rovers.
Auchinleck’s West of Scotland Premier Division rivals Clydebank tackle Annan Athletic.
There may be one all-Premiership tie between Livingston and Ross County.
All ties can be performed over the weekend of Saturday, 22 January.
Scottish Cup fourth-round draw
Peterhead v East Kilbride
Clydebank v Annan Athletic
Banks O’Dee v Raith Rovers
Motherwell v Inverness CT or Morton
Kelty Hearts or Montrose v St Johnstone
Livingston v Ross County
Dumbarton v Dundee
Aberdeen v Edinburgh Metropolis
Rangers v Stirling Albion
Ayr United v St Mirren
Kilmarnock v Dundee United
Hibernian v Cove Rangers or Queen of the South
Partick Thistle v Airdrieonians
Auchinleck Talbot v Hearts
Alloa Athletic v Celtic
Arbroath v Brechin Metropolis or Darvel