The letter doesn't specify an office though Johnston's manager, Tank Jones, has said Johnston's interested in a run for mayor or City Council. He did not immediately return a message Monday.
Wasilla is where Palin got her political start, first as a council member and then as mayor.
Earlier this month, Jones confirmed that Johnston planned to run for office as part of a reality TV show.
Johnston and Palin's daughter Bristol were thrust into the national spotlight in 2008, when Palin was making her vice presidential run and the two were unwed expectant teens.
Johnston, 20, has had a prickly relationship with the Palin family since the birth of son Tripp and has sought to capitalize on his notoriety, posing for Playgirl and hitting the Hollywood circuit. He and Bristol Palin recently broke off a short-lived engagement.
The filing was first reported by TMZ.com.