  We discuss $\theta$-deformed Maxwell theory at first order in $\theta$ with
the help of the Seiberg-Witten (SW) map. With an appropriate field redefinition
consistent with the SW-map we analyse the one-loop corrections of the vacuum
polarization of photons. We show that the radiative corrections obtained in a
previous work may be described by the Ward-identity of the BRST-shift symmetry
corresponding to a field redefinition.
