ACT Policing detectives arrested the man on Sunday night in the ACT suburb of Parkes.
Police allege the fire during a protest last week was deliberately lit, and have also charged the man with damaging Commonwealth property.
He is due to face the ACT Magistrates Court on Tuesday.
Three other arrests were made by ACT Policing on Saturday, and the individuals faced court on Sunday.
Two were charged with assaulting a frontline service provider and the third was charged with hindering a territory official.
The confirmation of the charges came on the same day police arrested a man outside Old Parliament House for trespassing.
Social media footage shows the man being detained by police on Monday.
The 30 minute livestream shows protesters with chains around their hands in what appears to replicate slavery bonds.
The man is seen holding a shovel with burning coals when speaking to an officer, asking to undertake a smoking ceremony outside Old Parliament House.
One officer told the protesters police were happy for a smoking ceremony to proceed but it couldn't be done near the building, which remains closed after the fire.
Old Parliament House was closed after the front doors of the heritage-listed building were burnt causing potentially irreparable damage.
Police confirmed officials had agreed a small smoking ceremony could take place as part of a peaceful protest but said it got "a little bit out of hand".
Investigations continue into the fire as Australian Federal Police and ACT Policing working to identify other people involved in the fire.
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