He has previously played in MLB for the Colorado Rockies, Texas Rangers, and Chicago Cubs and in Nippon Professional Baseball (NPB) for the Saitama Seibu Lions.

On July 28, 2015, the Blue Jays traded him, along with José Reyes, Miguel Castro and Jeff Hoffman to the Colorado Rockies for Troy Tulowitzki and LaTroy Hawkins.

[6] In the game that evening, he made his MLB debut pitching a scoreless ninth inning in a win over the Blue Jays, the team that had traded him.

After spending time with the Triple–A Round Rock Express, Tinoco was selected back to the major league roster on September 1.

[14] On October 4, Tinoco gave up a home run to Aaron Judge, his 62nd of the season to break the long-standing AL record previously held by Roger Maris.

On November 10, Tinoco was removed from the 40-man roster and sent outright to Triple–A; he elected free agency the same day.

[15][16] On December 16, 2022, Tinoco signed with the Saitama Seibu Lions of Nippon Professional Baseball (NPB).

[22] On June 25, 2024, Tinoco signed a minor league contract with the Kansas City Royals.