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. He spent five seasons with FC Dallas, winning U.S. Open Cup titles, before being traded to the Colorado Rapids. In his full-debut season, Moor helped the Rapids win MLS Cup 2010, the club's first league championship title. In 2016, signed with Toronto FC and spent four seasons with the club before returning to the Rapids in 2020. 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.