  We propose a new technique for weak gravitational lensing in the radio band
making use of polarization information. Since the orientation of a galaxy's
polarized emission is both unaffected by lensing and is related to the galaxy's
intrinsic orientation, it effectively provides information on the unlensed
galaxy position angle. We derive a new weak lensing estimator which exploits
this effect and makes full use of both the observed galaxy shapes and the
estimates of the intrinsic position angles as provided by polarization. Our
method has the potential to both reduce the effects of shot noise, and to
reduce to negligible levels, in a model-independent way, all effects of
intrinsic galaxy alignments. We test our technique on simulated weak lensing
skies, including an intrinsic alignment contaminant consistent with recent
observations, in three overlapping redshift bins. Adopting a standard weak
lensing analysis and ignoring intrinsic alignments results in biases of 5-10%
in the recovered power spectra and cosmological parameters. Applying our new
estimator to one tenth the number of galaxies used for the standard case, we
recover both power spectra and the input cosmology with similar precision as
compared to the standard case and with negligible residual bias, even in the
presence of a substantial (astrophysical) scatter in the relationship between
the observed orientation of the polarized emission and the intrinsic
orientation. Assuming a reasonable polarization fraction for star-forming
galaxies, and no cosmological conspiracy in the relationship between
polarization direction and intrinsic morphology, our estimator should prove a
valuable tool for weak lensing analyses of forthcoming radio surveys, in
particular, deep wide field surveys with e-MERLIN, MeerKAT and ASKAP and
ultimately, definitive radio lensing surveys with the SKA.
