"It's true. I'm a supermodel. I'm on the cover of these magazines - I'm on the cover of the biggest magazines," Trump told the crowd of around 4,500.
Trump later added: "It's not about me ... I'm doing a good job as a messenger. But I'm a messenger."
Trump had earlier praised former Arizona governor Jan Brewer - who signed a strict immigration measure in 2010 as governor and has been a staunch supporter of the presumptive GOP nominee - as "an amazing person."
"You know, it's not nice to say about a woman, but you are tough, aren't you?" Trump said. "She is tough, she's smart," he said.
Before the event, Brewer took the stage and pronounced to the crowd: "We need to keep Arizona red!"
Trump was introduced on the stage by Maricopa County Sheriff Joe Arpaio, who is a longtime, forceful critic of illegal immigration. Last month, a federal judge hold him in contempt along with his sheriff's office for continuing law enforcement practices previously found by the judge to be racial profiling.
Arpaio addressed the crowd from the stage before Trump's arrival and took a potshot at current Arizona Gov. Doug Ducey for not publicly backing Trump by name. Ducey has said he would support the nominee but has not appeared in public with Trump.