Montgomery County police spokesman Capt. Paul Starks says Glover and others stepped past yellow police tape and were asked to step back three times at Sodexo headquarters. When they refused, Starks says officers arrested them.
The dozen were issued citations for trespassing and let go. Starks says they face a $1,000 fine or 90 days in jail.
Starks says organizers told police beforehand that some would risk arrest.
The Service Employees International Union was protesting what it calls Sodexo's unfair and illegal treatment of workers. Sodexo says the union was spreading misinformation.
A publicist for the "Lethal Weapon" actor declined to comment.