First Division clubs Dundee and Queen of the South received byes into the second round.
Rangers are the trophy holders, having beaten Dundee United in a penalty shoot-out after a thrilling 2-2 draw at Hampden in March.
Co-operative Insurance Cup - first round draw:
Montrose v Cowdenbeath
Ross County v Airdrie United
Dumbarton v Annan Athletic
Peterhead v Dunfermline
Stranraer v Morton
Alloa Athletic v Elgin City
Clyde v Queen's Park
Albion Rovers v Raith Rovers
Ayr United v Berwick Rangers
East Fife v Brechin City
Arbroath v Stirling Albion
Partick Thistle v Forfar Athletic
East Stirlingshire v Livingston
Stenhousemuir v St Johnstone
Ties to be played on 5 & 6 August.