  We demonstrate that the intrinsic alignment of galaxies with large-scale
tidal fields sources an extra contribution to the recently-detected
cross-correlation of galaxy shear and weak lensing of the microwave background.
The extra term is the analogy of the 'GI' term in standard cosmic shear
studies, and results in a reduction in the amplitude of the cross-correlation.
We compute the intrinsic alignment contribution in linear and non-linear
theory, and show that it can be at roughly the 15% level for the CFHT Stripe 82
redshift distribution, if the canonical amplitude of intrinsic alignments is
assumed. The new term can therefore potentially reconcile the apparently low
value of the measured cross-correlation with standard LCDM. We discuss various
small-scale effects in the signal and the dependence on the source redshift
distribution. We discuss the exciting possibility of self-calibrating intrinsic
alignments with a joint analysis of cosmic shear and weak lensing of the
microwave background
