The Florida Marlins drafted Adduci in the 42nd round of the 2003 Major League Baseball draft. He made his professional debut in 2004 with the Rookie–level Gulf Coast Marlins, batting.207 in 49 games. Adduci remained with the Gulf Coast team during the 2005 season, batting.378 in only 11 games. Adduci again saw limited action during the 2006 season, appearing in 12 games for the Gulf Coast Marlins and only two games for the Single–A Greensboro Grasshoppers. In September, he was acquired by the Chicago Cubs.
Chicago Cubs
Now in Chicago's minor league system, Adduci split the 2007 season between the Peoria Chiefs and the Daytona Cubs. He spent the majority of the season with Peoria, batting.292 over 107 games, and tallying two home runs, 48 runs batted in, and 20 stolen bases. In 12 games with Daytona, Adduci batted.121. He spent the 2008 season in the Florida State League with Daytona, appearing in 123 games. He posted a.290 batting average, hit three home runs, drove in 48 runs, and stole 26 bases. Adduci was promoted to the Class AA Tennessee Smokies for the 2009 season. He batted.300 over 131 games, with four home runs, 51 RBI, and 35 steals. He also appeared in 20 games for Naranjeros de Hermosillo of the Mexican Pacific Winter League, where he hit for a.224 average.
Texas Rangers
On November 12, 2012, Adduci signed a minor league deal with the Texas Rangers. He spent the 2013 season with the Triple-A Round Rock Express, and made his major league debut on September 1, 2013.
Lotte Giants
On July 1, 2016, the Lotte Giants put Adduci on waivers after he tested positive for a banned substance, the pain medication oxycodone. Adduci was banned for 36 games, resulting in Adduci leaving the KBO League. The Giants were later fined 10 million won for inadequate player management as a result.
Detroit Tigers
On January 10, 2017, Adduci signed a minor-league contract with the Detroit Tigers. On April 23, 2017, the Tigers recalled him from the Triple-A Toledo Mud Hens to replace the injured JaCoby Jones. Adduci was placed on the 10–day disabled list on May 12, 2017. Following a rehab assignment in Toledo and the trade of Tiger outfielder J. D. Martinez on July 18, Adduci was recalled to the Tigers and joined them for a July 19 game against the Kansas City Royals. He elected free agency on November 6, 2017, and signed a new minor league contract with the Tigers on December 5. After starting the 2018 season in AAA Toledo, Adduci was called up to the Tigers on July 2. With both Miguel Cabrera and John Hicks having been placed on the disabled list during the year, Adduci played the majority of his games as the Tigers' first baseman. He finished the 2018 season hitting.267 with 3 home runs and 21 RBI in 176 at-bats.
Chicago Cubs (second stint)
On December 18, 2018, Adduci signed a minor league deal with the Chicago Cubs. His contract was selected by the Cubs on May 27, 2019 and he was added to the 40 man MLB roster. On June 3, 2019, the Cubs designated Adduci for assignment in order to open up a roster spot for former Cleveland outfielder Carlos González. He elected free agency on October 1.
Texas Rangers (second stint)
On March 14, 2020, Adduci signed a minor league deal with the Texas Rangers.
