Taking into account both curvature and disorder, we study the magnetic moments of carbon nanotori in the presence of magnetic field B (perpendicular to the torus plane). Due to the intrinsic curvature effect, energy gaps of about 10meV are obtained in those primary metallic carbon nanotori, which result in a novel magnetic response, depending on its chirality. An armchair carbon nanotorus exhibits a diamagnetic response in the vicinity of zero magnetic field, while the primary metallic zigzag nanotorus presents a much weaker paramagnetic response. This result differs substantially from previou...