His ancestor, Johann Casper Richter von Kronenscheldt, immigrated from Leipzig. He was the grandfather of Arent S. Crowninshield. Born in Salem, Massachusetts, he was first a businessman.
He was an unsuccessful candidate for election to Congress in 1798 (to fill the vacancy caused by the resignation of Dwight Foster) and then served in the Massachusetts State Senate in 1801. He was tendered the position of U.S. Secretary of the Navy by President Thomas Jefferson, but never entered upon his duties on account of ill health. He was elected as a Democratic-Republican to the 8th, 9th and 10th Congresses and served from March 4, 1803, until his death in Washington, D.C., aged 38.
While in the House, in the 9th Congress, he was chairman of the United States House Committee on Commerce and Manufactures. He is buried in Harmony Grove Cemetery in his hometown of Salem. In 1796, Hon. Jacob Crowninshield married Sarah Gardner, daughter of John (a direct descendant of an old planter) and Sarah (Derby - daughter of Richard (1712–1783)).
Their daughter Sarah married the Salem merchant Richard Saltonstall Rogers. After Sarah's death, Rogers married in 1847 Elizabeth Leavitt Pickman, daughter of Salem merchant Dudley Leavitt Pickman.