We report the detection of linearly polarized emission at 53 and 89 m from the radio-loud active galactic nucleus (AGN) Cygnus A using High-resolution Airborne Wideband Camera-plus (HAWC+) on board the Stratospheric Observatory For Infrared Astronomy (SOFIA). We measure a highly polarized core of 11 3% and 9 2% with a position angle (PA) of polarization of 43° 8° and 39° 7° at 53 and 89 m, respectively. We find (1) a synchrotron-dominated core with a flat spectrum (+0.21 0.05) and a turnover at 543 120 m, which implies synchrotron emission is insignificant in the infrared (IR), and (2) a 2-500 m bump peaking at ∼40 m described by a blackbody component with color temperature of 107 9 K. The polarized spectral energy distribution (SED) has the same shape as the IR bump of the total flux SED. We observe a change in the PA of polarization of ∼20° from 2 to 89 m, which suggests a change of polarization mechanisms. The ultraviolet, optical, and near-IR (NIR) polarization has been convincingly attributed to scattering by polar dust, consistent with the usual torus scenario, though this scattered component can only be directly observed from the core in the NIR. By contrast, the gradual rotation by ∼20° toward the far-IR (FIR), and the near-perfect match between the total and polarized IR bumps, indicate that dust emission from aligned dust grains becomes dominant at 10-100 m, with a large polarization of 10% at a nearly constant PA. This result suggests that a coherent dusty and magnetic field structure dominates the 10-100 m emission around the AGN.