Polarization measurements of the radio Arc were made with the VLA at 15 GHz. High frequency polarimetry made with high spatial resolution minimizes Faraday depolarization and reveals polarized filaments which correspond to the predominant filaments of the radio Arc. We notice a peculiar linear feature in the polarization map (“thorns”) which suggests the presence of a second magnetic field system. The total intensity maps show no evidence for an interaction between the two field systems, so the thorns may be foreground magnetized structures. However, if the two magnetic field systems do interact, it would allow a model in which the acceleration of relativistic particles takes place at their intersection. The accelerated particles would flow toward both ends of the radio Arc, and account for the intrinsic polarization observed along the entire length of the system. Thermal electrons responsible for the Faraday depolarization occuring at longer wavelengths may be supplied by the interaction of the streams of relativistic particles with relatively dense, ambient thermal clouds.