We investigate the geometry of the magnetic field towards the Radcliffe Wave, a coherent 3-kpc-long part of the nearby Local Arm recently discovered via three-dimensional dust mapping. We use archival stellar polarization in the optical and new measurements in the near-infrared to trace the magnetic field as projected on the plane of the sky. Our new observations cover the portion of the structure that is closest to the Sun, between Galactic longitudes of 122{deg} and 188{deg}. The polarization angles of stars immediately background to the Radcliffe Wave appear to be aligned with the structure as projected on the plane of the sky. The observed magnetic field configuration is inclined with respect to the Galactic disk at an angle of 18{deg}. This departure from a geometry parallel to the plane of the Galaxy is contrary to previous constraints from more distant stars and polarized dust emission. We confirm that the polarization angle of stars at larger distances shows a mean orientation parallel to the Galactic disk. We discuss implications of the observed morphology of the magnetic field for models of the large-scale Galactic magnetic field, as well as formation scenarios for the Radcliffe Wave itself.