United will open the defence of their trophy against a team they have beaten in their previous three domestic cup campaigns.
Peter Houston's men defeated County 3-0 at Hampden in May and clinched a 2-1 victory after extra-time at Dingwall in the Co-operative Insurance Cup in September.
Rangers have been handed a potentially difficult tie against in-form Kilmarnock at Ibrox.
Rangers needed Kenny Miller to complete a hat-trick after beating 10-man Killie 3-2 with the help of two penalties in the Clydesdale Bank Premier League on Saturday.
Celtic will face Berwick Rangers with the tie scheduled to be held at Shielfield Park.
Fourth round draw:
Aberdeen v East Fife
Dundee United v Ross County
Queen of the South v Brechin City or Annan Athletic
Montrose v Dunfermline Athletic
Greenock Morton v Airdrie United or Beith
Falkirk v Partick Thistle
Berwick Rangers v Celtic
East Stirlingshire v Buckie Thistle
Rangers v Kilmarnock
Hibernian v Ayr United
Stenhousemuir or Threave Rovers v Stranraer
Hamilton Academical v Alloa Athletic
St Mirren v Peterhead
Inverness Caledonian Thistle v Elgin City
Dundee v Motherwell
Heart of Midlothian v St Johnstone
Ties will be played on 8th and 9th January 2011
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