The Independence (USL) shut out the Charlotte Eagles (PDL) 2-0 to advance from the second round earlier in the week on Tuesday.
“The US Open Cup is a competition we take seriously,” RailHawks head coach Colin Clarke said.
“We’ve had great success and a lot of great results over the years, so we are definitely looking forward to start with this year’s competition.”
The RailHawks will seek to avenge a 1-0 Open Cup loss to the Independence in 2015.
Clubs that advance to the fourth round will compete against Major League Soccer (MLS) sides.
In representing the North American Soccer League (NASL), the RailHawks have had success in U.S. Open Cup play in recent years advancing deep into the tournament and defeating MLS squads Chivas USA and the LA Galaxy.