Upon the admission of Michigan as a State into the Union, Norvell entered the U.S. Senate with the Jacksonian wing of the Democratic-Republican Party. He served one term in the 24th, 25th, and 26th Congresses from January 26, 1837, to March 4, 1841. He did not seek reelection and resumed the practice of law in Detroit. Norvell was a member of the State senate in 1841 and of the State house of representatives in 1842. He served as United States district attorney in Michigan from 1846 to 1849.