Constable Kerr's mother, brothers and sister said the local and Assembly elections were "our only democratic means to reaffirm our need for peace".
"It doesn't matter which party we choose to vote for as long as they support the peace process," they said.
Constable Kerr was killed by a car bomb in Omagh, County Tyrone, on 2 April.
The 25-year-old had joined the PSNI just months earlier.
A group, made up of former members of the Provisional IRA, claimed responsiblity for the killing.'Opportunity'
In their statement, the Kerr family warned that by not voting "we are allowing the men of violence control and power over our lives".
"By exercising our democratic right to vote, we are condeming violence, ensuring power sharing and mutual respect and supporting law and order in our country," they said.
"We need politicians and a police force to represent and protect all sections of our community.
"We need to use this opportunity to have our say and we each have to take responsibility for ensuring we have a peaceful country, free of fear and intimidation and providing us all hope for the future."
Last month, a 33-year-old man was charged in connection with Constable Kerr's murder.
Gavin Coyle from Culmore Park, Omagh, was charged with possession of explosives, firearms and articles likely to be of use to terrorists at Dungannon Magistrate's Court.
The charges relate to items found in a police search in Coalisland following Ronan Kerr's death.
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