An online petition to "save the Dark Hedges" has gathered almost 3,000 signatures.
Since featuring in Game of Thrones, the 300-year-old beech trees that form a natural arch over a north Antrim road have attracted thousands of tourists to the area.
But Armoy woman Glenda Trolland, who started the petition, said that the large number of coaches of tourists and cars parking on grass verges were now threatening to destroy the landmark. She accused the authorities of doing little to protect the trees.
"I'd like a law to enforce the prohibition of parking on this road and instead to use the local hotel or lay-by to park in," she wrote.
"It is important in the interest of preserving the future of our trees."
The petition will be delivered to Causeway Coast and Glens Heritage Trust, which promotes and protects the area.