Hiram Rodney Burton (November 13, 1841 – June 17, 1927) was an American physician and politician from Lewes, in Sussex County, Delaware.

He attended St. Peter's Academy at Lewes, taught for two years in the schools in Sussex County, and engaged in the dry goods business in Washington, D.C., from 1862 until 1865.

Burton graduated from the medical department of the University of Pennsylvania in Philadelphia in 1868 and practiced medicine in Frankford, Delaware, from 1868 until 1872, when he moved back to Lewes.

From 1877 until 1888, Burton was the deputy collector of customs for the port of Lewes and was acting assistant surgeon in the Marine Hospital Service from 1890 until 1893.

He sought reelection in 1908 but lost his party's nomination to lawyer William H. Heald, who went on to win the general election and serve in Congress.