The Gers youngsters earned a place in the Second Round thanks to a 2-1 victory over St Johnstone at Ibrox.
Their reward is a home time with Dumbarton which will kick off at 1pm on the same day the first team face Montrose at Ibrox at 3pm.
The Youth Cup is now an under-20 competition, having changed from under-19 last term.
The Light Blues have reached the final in five of the last six years.
