Cingrani attended Lincoln-Way Central High School in New Lenox, Illinois. After graduating, he enrolled at South Suburban College, a junior college in South Holland, Illinois, before transferring to Rice University, where he played for the Rice Owls baseball team. In his junior year, his first at Rice, Cingrani struggled as a starting pitcher, pitching to an 8.59 earned run average (ERA) in six games started, issuing 16 walks and striking out only 13. After the season, he asked the coaches if they wanted him off the team due to his poor performance, but they told him they thought he could make progress.
Cingrani worked with Rice's coaches to change his mechanics during the offseason, which resulted in improved fastball velocity: from 86 miles per hour (138 km/h) before the changes to 90 to 94 miles per hour (145–151 km/h) after. However, he did not make the Owls' starting rotation due to the inconsistency of his off-speed pitches. Converted into a relief pitcher for his senior season, Cingrani tied the school record with 12 saves. He also had a 4–2 win–loss record, a 1.74 ERA and struck out 66 batters while walking only 10 in 57 innings pitched.
The Cincinnati Reds drafted Cingrani in the third round, with the 114th selection, of the 2011 Major League Baseball draft. He began his professional career with the Billings Mustangs of the Rookie-level Pioneer League, pitching in their starting rotation. He posted a 1.75 ERA in 13 games started.
Cingrani began the 2012 season with the Bakersfield Blaze of the Class A-Advanced California League, and received a mid-season promotion to the Pensacola Blue Wahoos of the Class AA Southern League. He led all of minor league baseball with a 1.73 ERA. The Reds promoted Cingrani to the major leagues on September 4, 2012. He made his major league debut on September 9, throwing three innings in relief.
After starter Johnny Cueto was placed on the disabled list, Cingrani was called up by the Reds on April 18, 2013 to take the starting rotation spot for Cueto until Cueto was reactivated. In July, Cingrani bounced between the rosters of the Cincinnati Reds and the Arizona League Reds. He was optioned to the AZL Reds on July 17, recalled on July 23, optioned on July 24, and recalled on July 28. He did not appear in any games for the AZL Reds during this period.
During spring training in 2015, the Reds announced that Cingrani would serve as a relief pitcher during the season.
The next two seasons for Cingrani would be mediocre for the lefty. with ERAs of 5.67 and 4.14 respectively.
The 2017 season for Cingrani wasn't much better. his ERA still sat at 5.40 while playing for the Cincinnati Reds.
Cingrani was traded to the Los Angeles Dodgers on July 31, 2017, in exchange for outfielder Scott Van Slyke and minor league catcher Hendrik Clementina.