Sheridan will challenge the current Maricopa County Sheriff Paul Penzone, a Democrat and former Phoenix police officer, who ousted Arpaio in 2016.
Arpaio, who calls himself "America's toughest Sheriff," was in the post for Maricopa County for 24 years.
He gained national notoriety for his treatment of those he held in an infamous outdoor jail known as "Tent City," where he made people wear pink underwear and work in chain gangs.