Sunday’s draw set up an Old Firm last-four clash which will take place at Hampden Park on the weekend of 16-17 April.
The other semi-final will see Dundee United take on the winners of the quarter-final replay between Hibs and holders Inverness Caley Thistle, who drew 1-1 at Easter Road on Sunday.
That semi will also be played at the national stadium on the same weekend.
Celtic booked their place in the last four with a comfortable 3-0 home win over Morton on Sunday.
Rangers defeated Dundee impressively 4-0 on Saturday.
Celtic and Rangers last met last season when Ronny Deila’s side won 2-0 in the League Cup semi-final at Hampden.
Rangers will be aiming to be the first side from a lower division to win the Scottish Cup since East Fife in 1938.
The quarter-final replay between Inverness and Hibs will take place at Caledonian Stadium on 16 March.