 He served as chief legal adviser of the former sixth Federal prohibition district from 1927 to 1929, and served as U.S. Attorney for the Western District of Pennsylvania from November 7, 1929, to September 1, 1933.He was special assistant to the United States Attorney General in the Pittsburgh vote-fraud cases (1934–1936).Graham was elected as a Republican to the Seventy-sixth Congress in 1938 and to the seven succeeding Congresses.