He began his political career in 1885 as a Republican member of the Woonsocket School Committee. He was appointed by Governor Taft to the 1889 Paris Exposition. Pothier was a member of the Rhode Island House of Representatives from 1887 to 1888, and served as city auditor from 1889 to 1894.
He was mayor of Woonsocket from 1894 to 1895, and declined renomination. From 1897 to 1898 he served as Lieutenant Governor of Rhode Island, during the first year that Elisha Dyer, Jr. was governor. After his term as lieutenant governor, he retired from public office, but returned as a member of the Rhode Island Board of Education in 1907. Governor Dyer appointed him to the 1900 Paris Exhibition.
Pothier was elected Governor of Rhode Island in 1908 and entered into service on January 5, 1909. He was reelected to three more one-year terms. At that time, biennial elections replaced annual elections for state officials, and Pothier won the first election for a two-year term as governor in 1912. He retired after this term, on January 5, 1915, when he was succeeded by fellow Republican Robert Livingston Beeckman. In 1915, retiring from politics, he became President of the Woonsocket Institute for Savings and the Providence Union Trust Company. He was again drafted by the Republican Party to run for governor in 1924. He won that election and reelection in 1926, serving from January 6, 1925 until his death on February 4, 1928. He was the first Rhode Island governor of French Canadian descent.