Mr O’Rourke, who is running for the Democratic nomination for president, had discussed his plans for gun control during a debate on Thursday night.
“Hell yeah, we’re going to take your AR-15,” the 46-year-old said to applause during the event.
The former Texas congressman also tweeted the phrase and is selling t-shirts featuring it as part of his campaign merchandise.
Mr O’Rourke’s full name is Robert Francis O’Rourke. “Beto” is a childhood nickname which he is known by.
“This is a death threat, representative,” Mr O’Rourke said. “Clearly, you shouldn’t own an AR-15—and neither should anyone else.”
Mr Cain dismissed the Democratic candidate’s criticism, branding him “a child”.
Banning assault weapons has been a key part of the 46-year-old’s election campaign after 22 people were killed when a gunman opened fire with a WASR-10 rifle at a Walmart store in El Paso, Mr O-Rourke's hometown, last month.
Other Democrats also took aim at the gun violence issue during the debate – Elizabeth Warren and Bernie Sanders both described corruption as a major obstacle to gun reforms.
Mr Sanders went on to say that he was not afraid of the National Rifle Association, an influential gun rights organisation.
A Republican-affiliated group, New Faces GOP, also paid for an advert attacking Alexandria Ocasio Cortez to air during the debates.
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The photo burns away to reveal a string of skulls behind the image.
“This is the face of socialism,” a voiceover says during the clip.
“Republicans are running TV ads setting pictures of me on fire to convince people they aren’t racist,” the congresswoman tweeted. “Life is weird!”
The first Democratic caucus is expected to take place in Iowa on 3 February 2020.