Parker was initially nominated to that court by President George W. Bush on May 9, 2001, to fill a seat vacated by Judge Ralph K. Winter, who assumed senior status on September 30, 2000. However, the Democratic-controlled United States Senate returned Parker's nomination just a few months later without considering it. Bush renominated him, along with many other previously returned nominees, on September 4, 2001. This time, the Senate confirmed Parker's nomination a little over a month later, on October 11, 2001, by a 100–0 vote.[3] He received his commission on October 16, 2001. He assumed senior status on October 10, 2009.[2]
On July 9, 2019, Parker was part of a three-judge panel which ruled that President Donald Trump cannot block people from his Twitter account for being critical of him. Writing for the panel, Parker said that the president uses his Twitter account to make official announcements and actions, so that responses to it are protected by the First Amendment. The decision affirmed an earlier ruling by U.S. District Judge Naomi Reice Buchwald.[4]