Before the raid, prosecutors had filed a complaint with a judge charging Robertson with making threats against the president, interstate threats, and threatening law enforcement officers.
Mr Biden is currently visiting the western United States and was scheduled to fly late on Wednesday from Albuquerque, New Mexico, to Salt Lake City.
In a social media post on Monday, Robertson wrote: “I hear Biden is coming to Utah. Cleaning the dust off the M24 sniper rifle. Welcom (sic), buffoon-in-chief!”
He had also made threats against Vice President Kamala Harris.
In one social media post last September he wrote: “The time is right for a presidential assassination or two. First Joe then Kamala!!!”
The complaint included pictures Robertson had posted of his guns, including one semi-automatic rifle he called a “Democrat eradicator”.
He also made threats against US Attorney General Merrick Garland and New York Attorney General Letitia James.
According to the complaint Robertson described himself as a “MAGA Trumper”.
Robertson had also made threats against Manhattan District Attorney Alvin Bragg.
In one social media post detailed in the complaint Robertson said he was heading to New York to “fulfill my dream of iradicating (sic)” Mr Bragg.