Holders St Johnstone have been drawn away to Kelty Hearts or Montrose in the Scottish Cup fourth round.
Rangers, who last won the trophy in 2009, will be fancied to go through when they take on Stirling Albion at Ibrox.
Celtic, who have won the competition a record 40 times, are away to Alloa Athletic.
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North Superleague side Banks O'Dee, who beat League One East Fife to reach the fourth round, were rewarded with a home tie against Championship side Raith Rovers.
West of Scotland Premier Division outfit Auchinleck Talbot, conquerors of Championship Hamilton in the last round, will welcome Hearts to Ayrshire in the last 32.
There is an all-Premiership tie between Livingston and Ross County.
St Johnstone will continue their defence of the cup playing during the weekend of January 22.
Scottish Cup fourth-round draw:
Peterhead v East Kilbride
Clydebank v Annan Athletic
Banks O'Dee v Raith Rovers
Motherwell v Inverness or Morton
Kelty Hearts or Montrose v St Johnstone
Livingston v Ross County
Dumbarton v Dundee
Aberdeen v Edinburgh City
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 City or Darvel