Randolph is a city in Riley County, Kansas, United States. As of the 2020 census, the population of the city was 159. Randolph was originally c…Randolph is a city in Riley County, Kansas, United States. As of the 2020 census, the population of the city was 159. Randolph was originally called Waterville, and under the latter name was laid out in 1856. It was renamed Randolph in honor Gardner Randolph, a pioneer settler.