Santiago graduated in 2006 from Bloomfield Tech High School in Essex County, New Jersey. He played one year at Okaloosa-Walton Community College (now Northwest Florida State College). He is of Puerto Rican descent.

Santiago was drafted by the White Sox in the 30th round of the 2006 Major League Baseball Draft. Santiago, who split time with the Winston-Salem Dash and Birmingham Barons in the first half of 2011, was called up to the Majors for the first time on June 26, 2011.

Santiago made his MLB debut on July 6, 2011, pitching a perfect ninth inning against the Kansas City Royals. He struck out Eric Hosmer for his first Major League strikeout. On April 7, 2012, Santiago earned his first career save by striking out Elvis Andrus to seal a 4–3 victory for the White Sox. On May 8, Santiago earned his first career win during a 5–3 victory over the Cleveland Indians, pitching one inning yielding two hits and striking out one. He remained the majority of the season in the bullpen while also starting on four occasions. He finished 4-1 in 42 games with 4 saves.

In 2013, Santiago split between the White Sox bullpen and the rotation, finishing with 23 starts while also appearing 11 times out of the bullpen. Although his ERA for the season was 3.56, his record was just 4-9 for the White Sox.

Santiago was traded to the Los Angeles Angels of Anaheim on December 10, 2013, in a three-team trade involving the Chicago White Sox, the Arizona Diamondbacks, and the Los Angeles Angels. The Angels received Tyler Skaggs along with Santiago, while the White Sox received Adam Eaton and the Diamondbacks received Mark Trumbo and two players to be named later. In his first season in Anaheim, Santiago was fairly inconsistent, he averaged less than 6 innings per start and for a moment was sent to the bullpen, where he made 6 appearances while also starting 24 times for the Angels. In 127.1 innings, Santiago went 6-9 with a 3.75 ERA.

Santiago enjoyed his best season in 2015, setting career highs in wins, innings, strikeouts, and in WHIP. He had the lowest ground ball percentage among major league pitchers (29.9%), and the highest fly ball percentage (53.6%).

On August 1, 2016, the Los Angeles Angels of Anaheim traded Santiago along with Alan Busenitz to the Minnesota Twins in exchange for Ricky Nolasco, Alex Meyer, and cash. For the Twins in 2016, he was 3-6 with a 5.58 ERA. Pitching for the two teams, he had the lowest line drive percentage allowed (15.9%) of all major league pitchers, the highest fly ball percentage allowed (50.0%), and gave up the highest percentage of hard-hit balls (37.3%).

He spent much of the 2017 season on the disabled list, and finished with a 4-8 record and a 5.63 ERA. He elected free agency on November 2, 2017.

Santiago played for the Puerto Rican national team in the 2017 World Baseball Classic where he won a silver medal.

On February 14, 2018, Santiago signed a minor-league deal with the Chicago White Sox. Santiago’s contract was purchased by the White Sox on March 28, and he was assigned to the Opening Day roster. Santiago spent the majority of the season in the White Sox bullpen, logging in 102 innings in 49 appearances.

On January 5, 2019, Santiago signed a minor league deal with the New York Mets. He was promoted to the major league club on May 20, following an injury to Seth Lugo. Santiago was designated for assignment on June 15, and elected free agency on June 18.

On June 21, 2019, Santiago signed a minor league deal with the Chicago White Sox. On August 6, the White Sox selected his contract.

On January 22, 2020, Santiago signed a minor league deal with the Detroit Tigers. Santiago was released by the Tigers organization on July 21, 2020.