Authors:Li et alAbstract:Magnetic fields (B-fields) play a key role in the formation and evolution of protoplanetary disks, but their properties are poorly understood due to the lack of observational constraints. Using CanariCam at the 10.4-m Gran Telescopio Canarias, we have mapped out the mid-infrared polarization of the protoplanetary disk around the Herbig Ae star AB Aur. We detect ~0.44% polarization at 10.3 micron from AB Aur's inner disk (r < 80 AU), rising to ~1.4% at larger radii. Our simulations imply that the mid-infrared polarization of the inner disk arises from dichroic emission of elongated particles aligned in a disk B-field. The field is well ordered on a spatial scale commensurate with our resolution (~50 AU), and we infer a poloidal shape tilted from the rotational axis of the disk. The disk of AB Aur is optically thick at 10.3 micron, so polarimetry at this wavelength is probing the B-field near the disk surface. Our observations therefore confirm that this layer, favored by some theoretical studies for developing magneto-rotational instability and its resultant viscosity, is indeed very likely to be magnetized. At radii beyond ~80 AU, the mid-infrared polarization results primarily from scattering by dust grains with sizes up to ~1 micron, a size indicating both grain growth and, probably, turbulent lofting of the particles from the disk mid-plane.