Police Scotland said spray paint had been used to damage the stonework at the site. It could take a week to remove and cost a four figure sum to repair, according to Historic Environment Scotland.
Scaffolding at abbey has been used to gain access to the building.
A police spokesman said “This is highly dangerous, and we would ask parents in the area to be fully aware of what your children are doing, where they are going, and who they are with.
“We would be particularly interested to hear from any parents whose children have come home in the evenings with paint on their clothes or smelling of solvent.”
The Declaration of Arbroath was written to Pope John XXII on behalf of the barons and community of the realm of Scotland.
The eloquent letter, written at Arbroath Abbey in support of King Robert Bruce (Robert I) and an independent Scotland, is still regarded as a spirited statement of a nation’s claim to freedom.
More to follow.