Two were also charged with arson offences and a ninth person was charged with outraging public decency, the force said in a statement.
Avon and Somerset Police said the investigation was ongoing with more charges expected to be brought soon.
Thousands of protesters gathered in Bristol city centre in late March for a sit-in to oppose the government’s controversial new policing bill.
A small minority of protesters later went on to attack the police station in Bridewell Street. As police vans were set alight and windows were smashed at the station, the force deployed riot officers and dogs to clear the streets.
Chief Superintendent Carolyn Belafonte of Avon and Somerset Police said Thursday’s charges were a “significant development” in the investigation into the night’s events.
“We remain resolute in our commitment to fully investigate offences committed in the vicinity of Bridewell police station and the wider city centre on the evening of Sunday 21 March and we anticipate there will be further people charged in the coming days and weeks as we continue to make further progress,” Chief Superintendent Belafonte said.
The “Kill the Bill” movement was sparked by the introduction of the Police, Crime, Sentencing and Courts Bill, which would grant officers more power to impose conditions on protests, including noise and time constraints.
The bill has passed its second reading in parliament and is now in committee stage, where MPs are given time to further scrutinise the contents.
Mostly peaceful protests have continued in many towns and cities around England and Wales, with large marches held on May Day in Bristol and London.