After attending Lakewood High School in Lakewood, California, Carp was drafted by the Mets in the ninth round of the 2004 Major League Baseball Draft. He hit 19 Home runs in only 313 at bats as a 19-year-old playing with the Hagerstown Suns, and won the Sterling Award as Mets organization player of the year following his season with the St. Lucie Mets. In that season he hit.287 with 69 runs scored, 27 doubles, one triple, 17 home runs and 88 runs batted in. In March 2007 he attended Major Leaguetraining campfor the first time, hitting.233 in 43 at bats with the Mets. His season with the Binghamton Mets of the Double-A Eastern League would be somewhat derailed by a broken finger, which he felt affected his swing even after returning from the disabled list. Carp hit.251/.337/.387/.725 with Binghamton. He played with the Scottsdale Scorpions of the Arizona Fall League during the fall. Carp enjoyed a great bounceback season in 2008, setting career highs in average, on-base percentage, OPS, doubles, homers, and walks. For the season, Carp hit.299/.403/.471/.874.
On February 20, 2013, Carp was acquired by the Boston Red Sox for a player to be named later or cash considerations. He made his Red Sox debut on April 7 versus the Toronto Blue Jays. On June 4, 2013, Carp earned his first career ejection for arguing a strike three call made by umpireAndy Fletcher. On September 11, 2013, Carp hit a go ahead grand slam to dead center off pitcher Roberto Hernandez of the Tampa Bay Rays to put ahead the Red Sox and eventually win the game in the 10th inning. Carp served as a backup first baseman, outfielder, and pinch hitter for the 2013 Red Sox, appearing in 86 regular season games and six postseason games as the team won the 2013 World Series. On April 24, 2014, in the ninth inning against the Yankees at Fenway Park, Carp appeared as a relief pitcher after the Red Sox had used all their relievers. Carp pitched one inning, allowing five bases on balls and one earned run. Shortly after the All-Star break, Carp requested that the Red Sox trade him. The request made news after the Red Sox traded veteran pitcher Jake Peavy to the San Francisco Giants on July 26. Carp was designated for assignment by the Red Sox on August 1.
Texas Rangers
Carp was claimed on waivers by the Texas Rangers on August 3, 2014. On August 30, the Rangers designated Carp for assignment. He elected free agency in October 2014.
On January 13, 2015, Carp signed a minor league deal with the Washington Nationals. He declined a minor league assignment in early April, and became a free agent.
On April 25, 2015, he signed a minor league contract with the Los Angeles Dodgers and was assigned to the Triple-A Oklahoma City Dodgers. He had only two hits in 22 at-bats for Oklahoma City and was released on May 7.