Billings was nominated by President Ulysses S. Grant on January 10, 1876, to a seat on the United States District Court for the District of Louisiana vacated by Judge Edward Henry Durell. He was confirmed by the United States Senate on February 10, 1876, and received his commission the same day. Billings was reassigned by operation of law to the United States District Court for the Eastern District of Louisiana on March 3, 1881, to a new seat authorized by 21 Stat. 507. His service terminated on December 1, 1893, due to his death in New Haven, Connecticut.
