Button Township was named for James Porter Button, Sr. (1822-1866), who served as township supervisor, justice of the peace, and county treasurer.

As of the 2020 census[1] there were 232 people, 109 households, and 67 families residing in the township.

There were 108 housing units at an average density of 3.17 per square mile (1.22/km2).

The racial makeup of the township was 98.71% White, 0.00% African American, 0.00% Native American, 0.00% Asian, 0.00% Pacific Islander, 0.00% from other races, and 1.29% from two or more races.

38.50% of all households were made up of individuals, and 3.70% had someone living alone who was 65 years of age or older.