Stoddard attended the Woodstock Academy from 1802 to 1803 and studied law at Brown University in Providence. In 1807 he graduated from there and was admitted to the legal profession in 1810. Stoddard practiced in West Woodstock.
He was elected as a member of the Democratic-Republican Party in Congress and represented there from March 4, 1821 until March 3, 1825 the state of Connecticut in the U.S. House of Representatives. After that Stoddard was from 1825 to 1827 at the Senate of Connecticut and in 1833 and again from 1835 to 1837 Vice- Governor of the state. After his retirement from politics, he began to work again in his former profession.
Stoddard died 1847 in West Woodstock and was buried at Bungay Cemetery.