McSally, a retired Air Force colonel, made the announcement in a YouTube video that highlighted her military experience and conservative credentials.
Arpaio is a sheriff known for his hardline and controversial border-security policies, as well as his ardent belief that former President Obama forged his birth certificate.
John Holden, a McSally supporter said, "if we get to the state level, the statewide level she should be able just to kick it".
"I absolutely refuse to bow down to Sharia law", McSally says, after a narrator discusses her successful fight against a USA military policy that required women to wear head-to-toe garb in Saudi Arabia.
"I speak a little salty behind closed doors at times as well, so I'm not going to throw the first stone on using any language", McSally said. "I think she's a lot conservative over the other choices".
The candidates will all be vying for the support of President Donald Trump, despite his low approval ratings, and McSally kickstarted her efforts to win his endorsement in her video by including a clip of the president saying, "my friend Martha McSally, she is the real deal. she is tough". Martha McSally Shows Off Her Pilot Skills Her action-packed announcement video trades on numerous same themes she used in her House campaigns, stressing her status of the first American female to fly in combat, winning a fight to refuse to don Muslim garb while serving in the Middle East, and as a congresswoman working to protecting funding for the locally produced A-10 fighter jet.
McSally, who served 26 years in the USA military, also used her experience to hit out at the Democrats in the Senate in the video, saying, "after taking on terrorists in combat, the liberals in the Senate won't scare me one bit".
A portion of her speech in Tucson would be spent praising Trump on several key policy accomplishments in his first year in office. "Our military is relying on us".
She also co-sponsored an immigration plan released by House conservatives this week that would reduce legal immigration levels by 25 percent, block federal grants to sanctuary cities and restrict the number of relatives that immigrants already in the US can bring here. The bill, which is unlikely to survive the GOP-controlled Senate, also provides temporary legal status for young immigrants enrolled in the Deferred Action for Childhood Arrivals, or DACA, program.
McSally, who has always been expected to run and is the preferred candidate of Senate GOP officials, launched her campaign with a slick 83-second video she posted online. Trump won Arizona in 2016 by less than 4 points.
But McSally makes a clear attempt to appeal to the party's right flank in her video, immediately reminding voters about her successful challenge to military rules that mandated women wear an Islamic robe over their uniform while in some Muslim countries.
"I absolutely refused to bow down to Sharia law", she said. "After eight years of fighting, I won my battle for the religious freedom of American servicewomen", she said.
The primary race won't be easy.
Democrats have another advantage: Their party's leading candidate, three-term incumbent Rep. Kyrsten Sinema, faces a relatively weak Democratic field, while McSally and her Republican opponents are expected to wage a bruising Republican contest until the state's late August primary elections.