Rice was born in East Otto, New York, on May 26, 1828; his schooling was private. He studied law, and upon his admission to the bar began practice in Irvine, Kentucky, in which state's house of representatives he served from 1855 to 1856. In 1856 he served as a presidential elector for the Republican ticket; in 1860 he moved to Minnesota, where he began service as a Union captain during the Civil War. Eventually he gained promotion to the position of judge advocate with the Minnesota Volunteers. In 1864 Rice settled in Little Rock, Arkansas and resumned his practice; he was active in organizing the Republican Party in the state, and was appointed the chair of a committee which in 1868 prepared the state's code of practice. Upon readmission of Arkansas to the Union Rice was elected to the Senate, serving from 1868 to 1873 and holding at one point the chairmanship of the Committee on Mines and Mining. On returning home Rice resumed his law practice; he moved to Colorado for health reasons in 1875, then back to Washington, D.C. in 1882, where he continued his practice until his death. He died in Tulsa, Oklahoma on January 19, 1905, and was buried in Washington's Oak Hill Cemetery.