Binary pulsars are affected by general relativity (GR), causing the spin axis of each pulsar to precess. We present polarimetric radio observations of the pulsar PSR J1906+ 0746 that demonstrate the validity of the geometrical model of pulsar polarization. We reconstruct the (sky-projected) polarization emission map over the pulsar's magnetic pole and predict the disappearance of the detectable emission by 2028. Two tests of GR are performed using this system, including the spin precession for strongly self-gravitating bodies. We constrain the relativistic treatment of the pulsar polarization model and measure the pulsar beaming fraction, with implications for the population of neutron stars and the expected rate of neutron star mergers.