  We discuss methods for performing weak lensing using radio observations to
recover information about the intrinsic structural properties of the source
galaxies. Radio surveys provide unique information that can benefit weak
lensing studies, such as HI emission, which may be used to construct galaxy
velocity maps, and polarized synchrotron radiation; both of which provide
information about the unlensed galaxy and can be used to reduce galaxy shape
noise and the contribution of intrinsic alignments. Using a proxy for the
intrinsic position angle of an observed galaxy, we develop techniques for
cleanly separating weak gravitational lensing signals from intrinsic alignment
contamination in forthcoming radio surveys. Random errors on the intrinsic
orientation estimates introduce biases into the shear and intrinsic alignment
estimates. However, we show that these biases can be corrected for if the error
distribution is accurately known. We demonstrate our methods using simulations,
where we reconstruct the shear and intrinsic alignment auto and cross-power
spectra in three overlapping redshift bins. We find that the intrinsic position
angle information can be used to successfully reconstruct both the lensing and
intrinsic alignment power spectra with negligible residual bias.
