Rovers progressed into the second round of the cup after beating newly promoted York City on penalties at the weekend.
The draw took place at 12:45 this afternoon and saw Rovers drawn at home against local side Hull City. The Tigers beat Rotherham United in the first round, again on penalties, to progress further in the competition.
Hull last visited the Keepmoat in pre-season, only a couple of weeks ago. They took the lead in the first half through a Rob Jones own goal before goals from Martin Woods (2) and trialist Amari Morgan-Smith in the second period secured a 3-1 win over the Championship side.
The tie will take place on the week commencing 27th August.