After his first term in the Indiana legislature and two unsuccessful campaigns for election to the U.S. Congress in 1838 and in 1840, Owen was elected as a Democrat to the U.S. House of Representatives in 1842. He served from 1843 to 1847 in the Twenty-eighth and Twenty-ninth Congresses. Owen was chairman of the Committee on Roads and Canals during the Twenty-eighth Congress. He was also involved in the debates about the annexation of Texas and an Oregon boundary dispute in 1844 that led to the establishment of the U.S-British boundary at the 49th parallel north, the result of the Oregon Treaty (1846).