According to the United States Census Bureau, the village has a total area of 0.3 square miles (0.9 km²), all of it land. Randolph is on the banks of the Missouri River. It is surrounded by Kansas City on all land borders, and the opposite side of the Missouri is also Kansas City.
There were 20 households out of which 15.0% had children under the age of 18 living with them, 55.0% were married couples living together, 15.0% had a female householder with no husband present, and 30.0% were non-families. 20.0% of all households were made up of individuals and 5.0% had someone living alone who was 65 years of age or older. The average household size was 2.35 and the average family size was 2.64.
In the village the population was spread out with 14.9% under the age of 18, 6.4% from 18 to 24, 38.3% from 25 to 44, 21.3% from 45 to 64, and 19.1% who were 65 years of age or older. The median age was 39 years. For every 100 females there were 123.8 males. For every 100 females age 18 and over, there were 110.5 males.
The median income for a household in the village was $53,750, and the median income for a family was $53,750. Males had a median income of $31,667 versus $35,000 for females. The per capita income for the village was $23,067. None of the population and none of the families were below the poverty line.