The Cubs also placed outfielder Justin Ruggiano on the 15-day disabled list with a left hamstring strain.
The moves mean the Cubs will have 13 pitchers.
"Right now, at least for 15 days with [Ruggiano] down [we'll have 13] and then we'll go from there," Cubs manager Rick Renteria said. "Right now, we can use the pitching."
Cubs starting pitchers have gone at least seven innings in each of the last three games, but both Edwin Jackson and Carlos Villanueva, who are starting Thursday and Friday, respectively, have not been able to go deep in games.
Renteria said they will use Emilio Bonifacio as an extra outfielder to make up for Ruggiano's absence.
Rosscup, 25, joins the Cubs roster for the second time this season. He served as the 26th man in the second game of a doubleheader April 16 at Yankee Stadium, and tossed 1 2/3 scoreless innings of relief. At Iowa, the lefty was 1-0 with a 4.26 ERA in five appearances.
Ramirez, 24, was acquired by the Cubs as the player to be named later in the five-player trade that sent Matt Garza to the Rangers last July.
He has a 7.71 ERA (six earned runs over seven innings) in six relief appearances for Iowa. This spring, Ramirez picked up two saves in eight relief outings, and threw 7 2/3 scoreless innings.
"I was surprised to get the call," Ramirez said. "I was just going about my business down there, trying to get better every day and that's what I'm going to try to do up here."
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.