Arpaio is known for his aggressive, and often controversial, position on immigration.
Cain drew criticism for his statements about immigration over the weekend, in which he suggested building an electrified fence on the border between the U.S. and Mexico. He later said his comments were a joke.
The former Godfather's Pizza CEO addressed the controversy during the press conference with Arpaio, telling reporters his comments weren't directed at people here legally.
"That wasn’t directed at people who are already here legally. It wasn't directed at them. So what's the beef? This is what I don't understand … I’m talking — that was directed at the people who are trying to sneak into America illegally," said Cain.
"Latinos that are here, I believe they deserve the same opportunities as every other citizen in this country.
"The ones that were offended because I want to keep illegals out, I'm not apologizing for that," he added.
According to Arpaio, Cain is the fourth candidate to seek his endorsement. Rep. Michele Bachmann (Minn.) also visited him in Arizona last month.
"I kind of like this guy, because he's unconventional, controversial, tells it like it is. Kind of like me," said Arpaio of Cain during the press conference.
For more on the meeting and influence of Arpaio in the presidential election, click here.