Burrows was a member of the Connecticut House of Representatives 1816–1820 and in 1826 and served as a delegate to the Connecticut constitutional convention in 1818. He was one of the commissioners to establish the boundary line between the States of Connecticut and Massachusetts. He was elected as a Democratic-Republican to the Seventeenth Congress (March 4, 1821 – March 3, 1823) but was not a candidate for renomination in 1822. After leaving Congress, he became a resident of Middletown 1823–1854. He was a surveyor and inspector of customs for the port of Middletown 1823–1847. He died in Mystic in 1858 and was buried in Elm Grove Cemetery.