Soria has played for his country’s Diablos Rojos del México (in the Mexican Baseball League) and Yaquis de Obregón in the Winter League. He played for the Class-A Fort Wayne Wizards as well. On December 9, 2006 in the Mexican Winter League, Soria threw a perfect game against the Naranjeros de Hermosillo.

In 2006, Soria was drafted at the age of 22 by the Kansas City Royals in the Rule 5 draft out of the San Diego Padres organization in 2006. He debuted for the Royals in the 2007 season, and had a record of 2–3 with 17 saves and an ERA of 2.48.

On May 17, 2008, Soria signed a 3-year, $8.75 million extension to his contract with the Royals, following his impressive performance as the team’s closer in the first quarter of the season.

Soria’s fantastic start led to him being selected to play in the 2008 Major League Baseball All-Star Game. Soria was the Royals’ lone representative in the All-Star Game. He was the first Royals closing pitcher to be named an All-Star since Mike MacDougal in 2003. He pitched 1⅔ innings, striking out the Florida Marlins’ Dan Uggla and New York Mets’ David Wright.

On May 26, 2010 Soria got his 100th save against the Texas Rangers. Soria was picked for the 2010 All-Star Game, the second of his career. He finished the season with a 1.78 ERA and 43 saves in 46 opportunities.

Soria struggled out of the gate in the 2011 season, blowing five of his first twelve save opportunities. After blowing saves on back to back days, Soria was replaced as closer by Aaron Crow on May 30. After a couple of good relief appearances in a non-closer role, Yost announced on June 6 that Soria had earned the position back.

Soria has been nicknamed The Mexicutioner, although in February 2011, he stated that he no longer wanted to be associated with that nickname due to violence in his home country.

On April 3, 2012, Soria underwent Tommy John surgery to repair a damaged UCL in his right elbow, causing him to miss the entire 2012 season. The Royals declined his 2013 option on October 31, making him a free agent.

On December 4, 2012, Soria signed a 2-year contract worth $8 million with the Texas Rangers with a club option for 2015. He started the season on the 60-day disabled list as he was still recovering from surgery. He made his first appearance for Texas on July 7, 2013. After former closer Joe Nathan signed with the Detroit Tigers in the offseason, Soria was named the new Rangers closer for the 2014 season.

On July 23, 2014, the Texas Rangers traded Soria to the Detroit Tigers in exchange for pitchers Jake Thompson and Corey Knebel. On July 22, 2015, Soria recorded his 200th career save.

On July 30, 2015, the Tigers traded Soria to the Pittsburgh Pirates in exchange for JaCoby Jones.

On December 10, 2015, Soria signed a 3-year, $25 million contract to return to the Royals.

On January 4, 2018, Soria was traded to the Chicago White Sox in a three team trade that also sent Jake Peter and Scott Alexander to the Los Angeles Dodgers, Luis Avilán to the White Sox and Trevor Oaks and Erick Mejia to the Royals.

On July 26, 2018, Soria was traded to the Milwaukee Brewers in exchange for Kodi Medeiros and Wilber Pérez. Soria declined his half of a mutual option for 2019 and became a free agent, on October 30, 2018.

On December 21, 2018, Soria signed a two year contract with the Oakland Athletics. On June 25, 2019, Soria pitched in his 674th Major League game, passing Dennys Reyes for the most by a Mexican-born pitcher.