Quoting an anonymous law enforcement official, the outlet said Roberto Minuta, of New York, would appear in court on Monday after he was arrested by the Federal Bureau of Investigations on the weekend.
Mr Minuta was first seen on video with Mr Stone, a Donald Trump adviser and pardon recipient, in Washington DC just hours before the Capitol was breached by rioters.
In the video, posted by ABC News, Mr Stone is talking to a woman as men wearing Oath Keeper insignia stand in the background.
In a comment to ABC, Mr Stone said: "I had no advance knowledge of the riot at the Capitol. I could not even tell you the names of those who volunteered to provide security for me, required because of the many threats against me and my family."
The Oath Keepers reportedly provided security for Stone while in Washington DC, although ABC does not suggest the men seen in the video were part of the mob that stormed the Capitol building.
At least five people associated with the Oath Keepers have been arrested on charges related to events at the Capitol, with three charged with conspiracy.
Mr Minuta, a 36-year-old tattoo artist, was arrested at a business in the Newburgh area of New York on Sunday, according to NBC News 4 New York.
Another man, 32-year-old Isaac Sturgeon, of Montana, was arrested in New York at JFK Airport after returning from Kenya on Saturday, the outlet reported.
He allegedly flew to Kenya on 24 January after his photo was added to the FBI's wanted page, but was ordered deported by Kenyan officials, according to court documents cited by the outlet.
Quoting law enforcement officials, Mr Sturgeon was allegedly seen on bodycam footage shoving barricades at police. He was expected to appear in Brooklyn federal court on Monday.
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