Respect Arizona will need to collect more than 350,000 valid signatures in the next 120 days to force a recall election.
The 80-year-old Arpaio was elected in November to his sixth consecutive term in office.
He filed paperwork last week indicating that he plans to run again in 2016.
In a statement Thursday, Arpaio say he believes the recall effort is over his stance on enforcing laws including those pertaining to illegal immigration.
Arpaio says if people insist on a recall drive, he believes county voters will back him.
Statement by Joe Arpaio
"I believe this effort is underway because of my stance on enforcing all the laws of our state including those pertaining to illegal immigration. I have expressed a sincere desire to work with all members of our community towards common goals and have extended the olive branch even to those activists who have voiced such hate towards me. Still, if these people insist on a recall drive, I have faith in the people of Maricopa County. They know exactly what and who they want in office and they won't be fooled by outside special interests."