In May 1992, Wilkins was in a rented vehicle with three other family members when they were pulled over by Maryland State Police for violating the speed limit. At the time, the Maryland State Police Department instructed their officers to focus on black males in expensive vehicles when conducting traffic stops.Democratic Governor William Donald Schaefer oversaw the Maryland State Police Department during this racial profiling era from 1987 until 1995 when he finally left office. Wilkins filed suit in the case of Wilkins v. Maryland State Police and eventually won a "landmark" settlement against the state of Maryland. As part of the case settlement, Maryland was required to maintain records of all traffic stops that resulted in vehicle search requests. The case helped bring national attention to the practice of racial profiling and helped popularize the term "driving while black".
On June 4, 2013, President Obama nominated Wilkins to serve as a United States Circuit Judge on the United States Court of Appeals for the District of Columbia Circuit, to the seat vacated by Judge David B. Sentelle, who took senior status on February 12, 2013. On October 31, 2013, the United States Senate Committee on the Judiciary voted to report Wilkins' nomination to the floor of the United States Senate in a 10-8, party-line vote. On November 14, 2013, Senate Majority LeaderHarry Reid motioned to invoke cloture on Wilkins' nomination, seeking to end a filibuster of his nomination by Senate Republicans. The Senate failed to invoke cloture on November 18, 2013 by a vote of 53-38, with 1 senator voting "present". Reid planned to hold a vote on Wilkins' nomination before the Senate adjourned for the year on December 20, but the vote did not take place. Cloture was subsequently invoked on January 9, 2014 by a vote of 55-38, with 1 senator voting "present". He was confirmed by the United States Senate 55-43 on January 13, 2014. His confirmation marked the first time the U.S. Court of Appeals for the D.C. Circuit had a full complement of judges in over 22 years since Clarence Thomas left the court on October 23, 1991 upon his joining the United States Supreme Court. He received his commission on January 15, 2014. After the death of Justice Antonin Scalia on February 13, 2016, Wilkins' name was among those mentioned by court-watchers as a possible successor. In April 2018, Wilkins wrote for the majority when it found that a Federal Trade Commission staff letter rejecting an earlier staff letter and concluding that use of soundboard technology violates the Telemarketing and Consumer Fraud and Abuse Prevention Act was not itself subject to judicial review under the Administrative Procedure Act, over the dissent of Judge Patricia Millett.