A relativistic model of pulsar polarization is presented which involves radio emission from the open field line region at radii well within the light cylinder. The model incorporates relativistic plasma flow when the corotation component of the plasma velocity is included. The model predicts that the centroid of the position angle curve arrives later than the centroid of the intensity profile by an amount 4r/c, where r is the emission radius. Our assumptions should hold for coherent curvature emission and for plasma maser emission mechanisms that do not employ a cyclotron resonance, as long as propagation effects are not too large. Application to pulsars with well-ordered position angle swings and periods between 0.06 and 3.7 s gives emission radii of not more than 2000 km for 0.43 and 1.4 GHz. In most cases, the upper bound is 100-300 km, and in 11 cases the emission radii are known within error bars of less than 50%. The results agree well with the emission radii predicted using a radius-to-pulse-width mapping. We find that the symmetry breaking effects of the corotation velocity may help explain a general asymmetry found in pulsar intensity profiles and may strongly affect the intensity profiles of short-period pulsars.