High school

Moore attended Mineola High School in Mineola, Texas, where he played both baseball and football. He batted .517 with a school-record 18 home runs, 63 RBI and 42 runs as a senior and was selected to the Texas High School Baseball Coaches Association 3A all-state team. Moore was also selected to the all-state team three times and named district Most Valuable Player as a junior and senior.

College

Moore played his junior college baseball at Northeast Texas Community College, where he earned first team all-Texas Eastern Athletic Conference honors in two seasons and earned Collegiate Baseball magazine national player of the week honors. He redshirted at University of Nebraska in 2005 and a year later, attended University of Texas at Arlington, where he was named the 2006 Southland Conference Newcomer of the Year and first team all-SLC selection. Moore went on to hit .350 with 10 home runs, 50 rbi, 89 hits, 22 doubles and five triples. ^[2]

Seattle Mariners

In Moore's first professional season in 2006, he combined to hit .281 with seven home runs and 33 RBIs in 228 at-bats in his split time between the Short-Season Everett Aqua Sox of the Northwest League and the Class-A Wisconsin Timber Rattlers of the Midwest League.

Moore spent all of his time in 2007 at the Class A level with the High Desert Mavericks. He finished third in the California League in RBIs with 102 and slugging percentage with a .543 clip. His 102 RBIs were second-most in the Mariners organization, while also finishing fifth with 22 home runs. Moore was named High Desert's Most Valuable Player by the Mariners. He was rated as the Mariners number 15 prospect by Baseball America. He participated in the Mariners 2007 Arizona Fall League.

Moore spent the entire 2008 season with the Double-A West Tenn Diamond Jaxx. He batted .319 in 429 at-bats with 60 runs scored, 34 doubles, two triples, 14 home runs and 71 RBIs. Moore was named a Southern League All-Star. He was sixth in batting average and sixth in doubles. Moore hit only .091 in 11 at-bats in the playoffs, and in the last game of the Diamond Jaxx' playoff run, fractured his left thumb. He was selected as West Tenn's MVP by the Mariners Player Development staff and named the number 19 prospect in the Southern League by Baseball America also selected by the publication as the Mariners' number six prospect.

Moore started the season with the West Tenn Diamond Jaxx but was later promoted to the Tacoma Rainiers of the Pacific Coast League. Moore finished the 2009 season batting a combined .287 with 12 home runs, 56 RBIs, 24 doubles in 118 games.

On September 13, 2009 Moore was called up to the Seattle Mariners, along with Tacoma teammates Matt Tuiasosopo and Garrett Olson.^[3] Moore was the only one of the three players called up who traveled from Sacramento, California, where Tacoma was eliminated from the Pacific Coast League playoffs against the Sacramento River Cats, to Arlington, Texas, where the Mariners were facing the Texas Rangers. Moore said this about the call-up:

This is so exciting, It's a dream come true...I got a little sleep on the flight, but I kept waking up with butterflies, knowing that I was coming back to Arlington, where I grew up watching games. Walking into this clubhouse, knowing that I am wearing a big league uniform now is really something....Oh yeah, I'm ready [to play], I'm ready for the opportunity to get out there, show them I believe in their stuff, get that good relationship with the pitching staff and just take them to victory.

— Adam Moore, mlb.com: September 13, 2009^[4]

Moore made his Major League debut on September 17, 2009. He went 0-for-5 against the Chicago White Sox, a game that went 14 innings. He played all 14 innings in that game and caught all 213 pitches that eight Mariners pitchers threw in the game.^[5]

Moore in the 2010 season.

Moore made the 25-man roster for the Mariners' 2010 campaign. He split time with other Seattle Mariner catchers Rob Johnson, Josh Bard and others.

On the April 7, 2011, Moore sustained a meniscus tear to his right knee and was out for two months.^[6]

On March 6, 2012, Moore broke the third metacarpal in his right wrist blocking a ball behind the plate. An examination the next day revealed the break. This cost Moore a chance to make the roster at the start of 2012.^[7] He was outrighted off of the 40-man roster on July 1.

Kansas City Royals

The Kansas City Royals claimed Moore off of waivers on July 7, 2012. He played in 35 games for the Triple A affiliate Omaha Royals, posting a .296 average with 22 RBI. He appeared in four games for Kansas City after being called up in September, going 2-for-11.^[8] On November 20, 2012 the Royals designated Moore for assignment as they cleared room on the 40-man roster ahead of the Rule 5 draft.^[8] He was released on August 8, 2013. On August 12, 2013, Moore was re-signed to a contract that will keep him within the Royals organization through 2014.

San Diego Padres

Moore was traded to the San Diego Padres on March 25, 2014.^[9] He was outrighted to the minors on November 3, 2014, and elected free agency.^[10]

Cleveland Indians

Moore signed a minor league deal with the Cleveland Indians on December 7, 2014. The Indians purchased his contract on September 23, 2015. He elected free agency on November 6, 2015.^[11] He re-signed with the Indians on November 19.

Moore was outrighted to the Triple–A Columbus Clippers on November 7, 2016.^[12] He elected free agency the following day. The Indians re-signed Moore to a minor league contract with an invitation to spring training on January 31, 2017.^[13] Moore played in 76 games for Columbus in 2017, hitting .238/.313/.369 with 8 home runs and 33 RBI. He elected free agency following the season on November 6.^[14]

Tampa Bay Rays

On February 3, 2018, Moore signed a minor league contract with the Tampa Bay Rays.^[15] Moore was designated for assignment on July 25, 2018. He had his contract purchased again on August 31, 2018. The Rays outrighted him to the minors on November 1, 2018 and he elected free agency.^[16]

Texas Rangers

On February 14, 2019, Moore signed a minor-league contract with the Texas Rangers and was assigned to the Triple-A Nashville Sounds.

Kansas City Royals (Second Stint)

On August 7, 2019, Moore was traded to the Kansas City Royals in exchange for cash and was assigned to the Omaha Storm Chasers. He became a free agent following the 2019 season.^[17]