From 1982 to 1986, he served as an assistant United States attorney in the District of Colorado.

In January 2004, he became the Federal Public Defender for the Districts of Colorado and Wyoming, serving until 2013.

[2][3] On November 14, 2012, President Barack Obama nominated Moore to serve as a United States district judge of the United States District Court for the District of Colorado, to the seat being vacated by Judge Wiley Young Daniel, who took senior status, effective January 1, 2013.

[2][3] On January 3, 2013, his nomination was returned to the President, due to the sine die adjournment of the Senate.

His nomination was reported by the Senate Judiciary Committee on February 14, 2013, by voice vote.