
The Jambos were held by the Jags in Monday’s clash at Firhill after Christophe Berra’s opener was cancelled out by Christie Elliott.
Should Craig Levein’s men win the replay on Tuesday, March 12, they will play Inverness at Hampden Park on the weekend of April 13.
The Caley Jags, who defeated Dundee United in the quarter-finals, are managed by Hearts’ record goalscorer and former manager John Robertson.
In the other semi-final, Aberdeen or Rangers will take on Celtic.