The Morton County Sheriff's Department opened a criminal investigation and charged Stein and Baraka with criminal trespassing and criminal mischief -- both are misdemeanors.
Beyond the photos and video showing Stein's actions, investigators say they have video of Baraka painting the word "decolonization" on the front of a bulldozer.
Seemingly in response to the charges, Stein tweeted, "The Dakota Access Pipeline is vandalism on steroids."
Protests at a pipeline construction site began weeks ago. The $3.8 billion pipeline will run from North Dakota to Illinois, and part of its path will cross the Missouri River. American Indian tribes worry a leak in the pipeline would taint their only source of water.
The same day the Green Party duo visited the protest site, a federal judge ordered construction to temporarily stop at some of the pipeline construction sites.
The maximum sentence for a class B misdemeanor in North Dakota is 30 days in jail, a $1,500 fine or both.