The Ibrox side have made a strong start to life under Mark Warburton after following up their 6-2 Petrofac Training Cup win over Hibernian with a 3-0 victory on Sunday.
Now they will face opposition from a lower league once again as they travel to nearby Lanarkshire to take on Gary Bollan’s Airdrie team.
Hearts will travel to Forfar Athletic while their Edinburgh rivals Hibs host Stranraer when the ties are played on August 25 and 26.
Three Premiership sides have home ties, with Kilmarnock playing Berwick, Partick taking on Falkirk and Ross County meeting Ayr United.
Hamilton go to Raith Rovers while Dundee will play Dunfermline at East End Park and Motherwell visit East Fife, one of two League Two teams still in the competition.
Queen of the South take on Championship rivals Morton while St Mirren clash with Livingston in the only ties where sides from the same league collide.
The 11 winners will advance to the third round, at which point five Premiership teams will enter the tournament for the first time.
Celtic, Aberdeen, Inverness and St Johnstone have all been exempt due to their involvement in European competitions while Dundee United, last season’s finalists, also received a bye.