Royce was born in Berkshire, Vermont, the son of Elihu Marvin and Sophronia (Parker) Royce. He was educated in the district schools and at academies in St. Albans and Enosburgh. He studied law with Thomas Childs, was admitted to the bar in 1844, and partnered with Mr. Childs for several years in his hometown. The University of Vermont conferred on him the honorary degree of Master of Arts in 1851, and Doctor of Laws (LL.D.) in 1882. He married, January 23, 1851, Mary T. Edmunds, of Boston, Massachusetts, who bore him three children.
He was state's attorney for Franklin County in 1846 and 1847, and represented Berkshire in the Vermont Legislature the latter year as well. He was a district delegate to the Whig National Convention in 1847. In 1849, 1850, 1851, 1861 and 1868, he was elected to the Vermont Senate from Franklin County.
In 1856 he was elected by a majority of 5,960 votes as a Republican Party representative to Congress from the Third district, becoming the youngest member of the Vermont contingent in Washington. He served two terms, from March 4, 1857 to March 3, 1861. During his first term he was a member of the Foreign Affairs Committee. He won a second term by a majority of 4,129 votes. During his second term, he wrote a part of the Foreign Affairs Committee report opposting annexation of Cuba, and delivered a speech in opposition to President James Buchanan's Cuban policy. Senator Jacob Collamer spoke out against the acquisition as well.
Royce did not run for a third term. He returned to his law practice until he was elected as an associate justice in the Vermont Supreme Court in 1870. He was appointed chief justice in 1882, replacing John Pierpoint, and served until 1890, when he resigned.
Royce died in St. Albans, and is interred in Cavalry Cemetery, East Berkshire.