Born in 1784 in Louisa County, Virginia, Crawford attended Hampden–Sydney College and read law.
He was United States Attorney for the District of Mississippi Territory starting in 1814.
He was confirmed by the United States Senate on May 22, 1826, and received his commission the same day.
Crawford was assigned by operation of law to additional and concurrent service on the United States District Court for the Middle District of Alabama on February 6, 1839, to a new seat authorized by 5 Stat.
His service terminated on February 28, 1849, due to his death in Mobile, Alabama.