Born in Dallas, Moor began playing college soccer for the Furman Paladins before transferring to the Indiana Hoosiers.

After three seasons with the Hoosiers, and helping the side with the 2004 College Cup, Moor was drafted in the first round of the 2005 MLS SuperDraft by FC Dallas with the 6th overall pick.

During his time at Toronto FC, Moor was part of the side which won MLS Cup 2017, the Supporters' Shield, and three Canadian Championship titles.

His last collegiate game was in the penalty kick thriller against UC Santa Barbara in the 2004 NCAA Finals in which Moor's Indiana was triumphant.

In 2007, Moor led the team with 28 starts and scored two goals including a game-winning header against the Colorado Rapids on August 4, 2007, in a 1–0 victory.

On August 31, 2009, Moor was traded to the Colorado Rapids along with a FC Dallas's second-round 2010 MLS SuperDraft pick and allocation money in exhangce for Ugo Ihemelu.

On October 23, 2020, an article from The Denver Post revealed that in late September 2020, Moor had taken up a temporary role as a player-coach with Colorado amid a COVID-19 outbreak that left the entire coaching staff unavailable.

[12] He played for the United States in 2007 Copa América and started for the men's national team in a friendly versus Mexico on February 6, 2008, where he assisted Jozy Altidore for his first international goal.