The Cubs got Turner from Miami on Friday in a trade for two minor league pitchers. The 23-year-old Turner was designated for assignment by the Marlins last week.
Turner is 4-7 with a 5.97 ERA in 20 games this season, and manager Rick Renteria said the right-hander's role would be determined after consulting with pitching coach Chris Bosio.
Chicago also sent pitcher Chris Rusin to Triple-A Iowa and placed reliever Brian Schlitter on the disabled list before its series finale against Tampa Bay. Schlitter is out with an inflamed right shoulder.
Ramirez had been out with a sore triceps. The 25-year-old rookie right-hander, who was acquired last season in a trade that sent starting pitcher Matt Garza to Texas, is 1-1 with three saves and a 0.96 ERA in 33 games this year.
Also Sunday, the Cubs announced outfielder Ryan Kalish had cleared waivers and was headed for Iowa. He was designated for assignment Friday to make room for Turner on the 40-man roster.