Royce was born in Tinmouth in the Republic of Vermont on August 12, 1787, the son of Stephen Royce (1764-1833), a veteran of the American Revolution and War of 1812, and Minerva (Marvin) Royce, a daughter of Ebenezer Marvin, who served as a judge and member of Vermont's Council of Censors. Royce grew up in Franklin and Berkshire and attended the local schools. He attended school in Tinmouth and graduated from the Addison County Grammar School. He began attendance at Middlebury College in 1804, where his classmates included Daniel Azro Ashley Buck and William Slade. He taught school in Sheldon to earn his tuition, and he graduated from Middlebury in 1807.