Riverton Township takes its name from the Buffalo River.

As of the census[2] of 2000, there were 462 people, 159 households, and 124 families residing in the township.

The population density was 12.9 people per square mile (5.0/km2).

There were 159 households, out of which 39.6% had children under the age of 18 living with them, 70.4% were married couples living together, 3.1% had a female householder with no husband present, and 22.0% were non-families.

16.4% of all households were made up of individuals, and 5.7% had someone living alone who was 65 years of age or older.