The Reds also transferred pitchers Trevor Bell (elbow) and Sean Marshall (shoulder) to the 60-day DL.
They activated right-hander Brett Marshall, who had been on the disabled list since March with a strained finger tendon, and optioned him to Louisville.
Diaz, 30, has pitched 12 seasons in the minor leagues without ever appearing in the majors. He has a 2-2 record with a 1.35 ERA in 30 games out of the bullpen for Louisville this season.
Cingrani is 2-8 with a 4.55 ERA in 13 games, including 11 starts, this season. He gave up two hits and three walks in 1 2/3 innings against Pittsburgh on Thursday, walking in the deciding run in the 12th inning.