On June 9, 2016, Carleton signed with Major League Soccer side Atlanta United FC as a Homegrown Player.
He spent the 2016 season on loan with United Soccer League side Charleston Battery.
 He made his first appearance on September 7, 2016 against FC Montreal.
On September 10, 2016, Carleton became the youngest American professional player in history to start a USL match.
On September 17, 2016, Carleton recorded his first professional assist for the Battery.

On February 11, 2017, he made his debut for Atlanta United and scored during the second half of the team's first preseason game against Chattanooga FC.

Carleton made his MLS debut on May 20, 2017 as an 85th minute substitution against Houston Dynamo.
The 16-year-old was given a standing ovation at a sold out Bobby Dodd Stadium.
Andrew provided his first career assist in a 4–1 win against Vancouver on March 17, 2018.

On April 21, 2018, while on loan to Atlanta United 2, Carleton scored his first professional goal, a penalty kick in a 1–1 draw against Louisville City FC.
He scored his first goal with Atlanta United's first team on June 6, 2018 vs Charleston Battery in the US Open Cup.

On January 24, 2020, Carleton was loaned to USL Championship side Indy Eleven for the 2020 season.
On June 9, 2016, Carleton signed with Major League Soccer side Atlanta United FC as a Homegrown Player. He spent the 2016 season on loan with United Soccer League side Charleston Battery.  He made his first appearance on September 7, 2016 against FC Montreal. On September 10, 2016, Carleton became the youngest American professional player in history to start a USL match. On September 17, 2016, Carleton recorded his first professional assist for the Battery.
On February 11, 2017, he made his debut for Atlanta United and scored during the second half of the team's first preseason game against Chattanooga FC.
Carleton made his MLS debut on May 20, 2017 as an 85th minute substitution against Houston Dynamo. The 16-year-old was given a standing ovation at a sold out Bobby Dodd Stadium. Andrew provided his first career assist in a 4–1 win against Vancouver on March 17, 2018.
On April 21, 2018, while on loan to Atlanta United 2, Carleton scored his first professional goal, a penalty kick in a 1–1 draw against Louisville City FC. He scored his first goal with Atlanta United's first team on June 6, 2018 vs Charleston Battery in the US Open Cup.
On January 24, 2020, Carleton was loaned to USL Championship side Indy Eleven for the 2020 season.
Andrew Carleton