Scottish Premier League champions Rangers will face Second Division side Arbroath in the fourth round of the Scottish Cup while the tournament holders Celtic travel to Peterhead.
The two Scottish giants both face away fixtures against their respective teams, which are due to take place during the weekend of January 7.
The 2006 Scottish Cup winners Hearts have been drawn to play junior non-league side Auchinleck Talbot, who will visit the capital.
Livingston, Queen of the South, and Motherwell are yet to learn their opponents as Ayr United, Montrose, Partick Thistle, Culter, Elgin City and Queens Park are due to compete before qualifying for the fourth round.
Fourth round Scottish Cup fixtures in full:
Ross County vs. Stenhousemuir
Livingston vs. Ayr Utd or Montrose
Raith Rovers vs. Greenock Morton
Hearts vs. Auchinleck Talbot
Cowdenbeath vs. Hibernian
St Johnstone vs. Brechin City
Stranraer vs. Aberdeen
Culter or Partick Thistle vs. Queen of the South
Inverness CT vs. Dunfermline
Falkirk vs. East Fife
Motherwell vs. Elgin City or Queens Park
Arbroath vs. Rangers
Peterhead vs. Celtic
Airdrie United vs. Dundee United
Dundee vs. Kilmarnock
St Mirren vs. Hamilton
Danielle Joynson
