The FBI agent in the court filing says the agency was tipped off by a former romantic partner of Ms Williams who alleged she had meant to take a laptop or hard drive from the office of Ms Pelosi, the Democrat Speaker of the House of Representatives.
The FBI says it was contacted by a person of interest claiming to be a "romantic partner" of Williams on its tip line.
According to a criminal complaint filed by an FBI Special Agent, Pennsylvania resident Riley June Williams is wanted on charges of entering a restricted building, disrupting the orderly conduct of government, and engaging in disorderly or disruptive conduct in relation to the breach of the Capitol Building on January 6.
Video from inside the Capitol Building during the January 6 riots appeared to show Williams directing protesters up a staircase that led to Pelosi's office.
The tipster added that they believed Williams was trying to get the device to a friend in Russian Federation, who would then sell it to SVR.
However, the witness allegedly told investigators the transfer of the device to Russian Federation "fell through for unknown reasons", and Williams was either still in possession of it or had destroyed it.
That staircase leads to Pelosi's office, Lund said. She had also changed her phone number and deleted a number of social media accounts, the Federal Bureau of Investigation said.
Investigators believe Williams has fled.
Woman who 'took laptop' from Pelosi's office in Capitol riot 'planned to sell it to Russian spies'
According to the FBI, Williams had driven down from Harrisburg to attend the January 6 "Stop the Steal" rally with her father, of Camp Hill. In the segment, the mother says that her daughter is not home.
The same woman can be seen in other video taken outside the Capitol building on January 6, according to the affidavit.
"According to the Harrisburg officers, on January 16, 2021, they again spoke with WILLIAMS' mother who told them that a British media crew had come to her home the night before, asking to speak with WILLIAMS, who was not present", the affidavit states.
The affidavit goes on to give details of an ITV News report from inside the Capitol building at the time of the siege, in which a woman identified as Ms Williams can be seen and heard directing the crowd to go up a staircase that leads to Ms Pelosi's office. "Her mother acknowledged that it was WILLIAMS in the image". The nature surrounding the report is unclear.
Among the items stolen while the seat of power in America was being ransacked was a laptop belonging to house speaker Nancy Pelosi. Some smashed furniture and scattered documents across the floor while others posed mockingly for photos at her desk.
More than 125 people have been arrested so far in connection with the attack on the Capitol, on charges from curfew violations to federal felonies, according to The Associated Press.
Five people - including a Capitol police officer - were killed in the riots.
The FBI and other law enforcement agencies continue to search for the identities of several other individuals who were photographed rioting in the Capitol.