The man, identified as Floyd Ray Roseberry, 49, surrendered hours after the threat was made.
US Capitol Police had been negotiating with the driver who had parked a pick-up truck near the Library of Congress, across the street from the Capitol building and Supreme Court.
His motives remain unknown. Police are still searching the vehicle.
Congress is currently in recess, but some staff are working in the Capitol. Several office buildings were evacuated.
Videos purporting to be the man livestreaming from the vehicle have been shared on social media. Facebook has deactivated the livestream and removed the profile.
In the video, the man addressed US President Joe Biden directly and spoke of revolution.
Mr Roseberry had parked the vehicle on a pavement and told an officer who approached him that he had a bomb, while holding what appeared to be a detonator, Capitol Police Chief J Thomas Manger told a news conference.
Police communicated with Mr Roseberry via a white board and used a robot to deliver him a telephone, which he did not use, Chief Manger said. Mr Roseberry then stepped out of the vehicle and surrendered.
"He gave up and did not resist and our folks were able to take him into custody without incident," Chief Manger said.
Police said they discovered possible bomb-making materials in the vehicle, but no bomb. Two law enforcement sources, who requested anonymity, told the Reuters news agency that it appeared Mr Roseberry had acted alone.
Federal agents raided Mr Roseberry's home in Grover, North Carolina, during the standoff.
Neighbours told Reuters that Mr Roseberry is a Republican who had been seen wearing a "MAGA" cap to show his support for former President Donald Trump.
Security was heightened around the Capitol after supporters of Mr Trump stormed the building on January 6. At least 535 rioters have been arrested since the attack.