As a member of the Oneonta Tigers, Moscoso pitched the second perfect game in New York–Penn League history in a 6–0 victory over the Batavia Muckdogs on July 15, 2007.

[1] Moscoso was acquired by the Texas Rangers from the Detroit Tigers along with pitcher Carlos Melo for catcher Gerald Laird on December 12, 2008.

On May 30, 2009, Moscoso made his major league debut against the Oakland Athletics, striking out 2 and pitching a scoreless ninth inning.

[2] After appearing in ten games in '09, Moscoso had an ERA of 3.21 through 14.0 innings pitched, giving up 15 hits, 7 runs, and 6 walks but also struck out a dozen.

[3] On May 24, 2011, he was recalled to the Oakland Athletics to take the place in the rotation of Tyson Ross, who went on the DL with a strained left oblique.

On January 16, 2012, Moscoso was traded, along with fellow pitcher Josh Outman, to the Colorado Rockies for outfielder Seth Smith.

On July 26, 2013, Moscoso was traded to the San Francisco Giants for a player to be named later or cash considerations.

On December 26, 2013, it was announced that Moscoso had signed with the Yokohama DeNA BayStars of Nippon Professional Baseball for 2014.