We report the first detection of galactic spiral structure by means of thermal emission from magnetically aligned dust grains . Our 89 \mu m polarimetric imaging of NGC 1068 with the High-resolution Airborne Wideband Camera/Polarimeter ( HAWC+ ) on NASA’s Stratospheric Observatory for Infrared Astronomy ( SOFIA ) also sheds light on magnetic field structure in the vicinity of the galaxy’s inner-bar and active galactic nucleus ( AGN ) . We find correlations between the 89 \mu m magnetic field vectors and other tracers of spiral arms , and a symmetric polarization pattern as a function of the azimuthal angle arising from the projection and inclination of the disk field component in the plane of the sky . The observations can be fit with a logarithmic spiral model with pitch angle of 16.9 ^ { +2.7 } _ { -2.8 } ^ { \circ } and a disk inclination of 48 \pm 2 ^ { \circ } . We infer that the bulk of the interstellar medium from which the polarized dust emission originates is threaded by a magnetic field that closely follows the spiral arms . Inside the central starburst disk ( < 1.6 kpc ) , the degree of polarization is found to be lower than for far-infrared sources in the Milky Way , and has minima at the locations of most intense star formation near the outer ends of the inner-bar . Inside the starburst ring , the field direction deviates from the model , becoming more radial along the leading edges of the inner-bar . The polarized flux and dust temperature peak \sim 3 - 6 \arcsec NE of the AGN at the location of a bow shock between the AGN outflow and the surrounding interstellar medium , but the AGN itself is weakly polarized ( < 1 % ) at both 53 and 89 \mu m .