The ferromagnetism in many carbon nanostructures is attributed to carbon dangling bonds or vacancies. This provides opportunities to develop new functional materials, such as molecular and polymeric ferromagnets and organic spintronic materials, without magnetic elements (for example, 3d and 4f metals). Here we report the observation of room temperature ferromagnetism in Teflon tape (polytetrafluoroethylene) subjected to simple mechanical stretching, cutting or heating. First-principles calculations indicate that the room temperature ferromagnetism originates from carbon dangling bonds and strong ferromagnetic coupling between them. Room temperature ferromagnetism has also been successfully realized in another polymer, polyethylene, through cutting and stretching. Our findings suggest that ferromagnetism due to networks of carbon dangling bonds can arise in polymers and carbon-based molecular materials.