In 2005, Marquez played for the Single-A Charleston RiverDogs. Making a team leading 27 starts, he went 9-13 with an ERA of 3.42. Marquez was second on the team to Chase Wright in wins (9), innings pitched (139+2⁄3), and strikeouts (107).
In 2007, Marquez played for the Double-A Trenton Thunder and was an Eastern League midseason All-Star for the team that year. Marquez went 15-9 with a 3.65 ERA for the Thunder. He led the league with 15 wins, was tied with 27 starts, was tied for second in innings pitched (155+1⁄3), tied for third in complete games (2), and was tenth in ERA (3.65).
On November 20, 2007, the New York Yankees purchased Marquez's contract, protecting him from the Rule 5 draft.
Marquez made his MLB debut on July 9, 2010, pitching the 9th inning vs. Kansas City allowing 2 runs in an 8-2 White Sox win. The White Sox recalled him on May 30, 2011.[2] He was designated for assignment on June 5.[3]
Return to Yankees
Marquez was claimed off waivers by the New York Yankees on June 8 and added to the MLB roster when Joba Chamberlain was placed on the DL.[4] On August 27, the Yankees outrighted Marquez to the Triple-A Scranton/Wilkes-Barre Yankees.[5] He was granted free agency in November 2011.
Seattle Mariners
On November 10, 2011, the Seattle Mariners signed Marquez to a minor league contract. He was released on July 24, 2012.
Colorado Rockies
He was signed by Colorado Rockies on Aug 11th, 2012, and assigned to Triple A Colorado Springs Sky Sox.
Cincinnati Reds
On January 2, 2013, he signed a minor league contract with the Cincinnati Reds but was released soon after.[6]