Woodcock attended the public schools, then studied law, was admitted to the bar, and practiced.

Woodcock was elected as a Democratic-Republican to the 17th United States Congress, holding office from December 3, 1821, to March 3, 1823.

After leaving Congress Woodcock resumed the practice of law.

After leaving Congress the second time, he again resumed the practice of law.

His daughter Mary was married to New York Attorney General Stephen B. Cushing.