Rodon is to start in place of Jeff Samardzija, who on Wednesday started serving a five-game suspension for his involvement in a bench-clearing brawl against Kansas City on April 23.
The 22-year-old left-hander made his major league debut on April 21 and has a 2.84 ERA in 6 1-3 innings and three relief appearances.
''He's doing well for a young guy coming up and I know it's been a tough spot for him to be able to fill some innings for us, come in and get a lefty,'' White Sox manager Robin Ventura said. ''Now, with this going on, he gets the chance to make a start for us. It's a good spot for him.''