  The detection of B-modes in the Cosmic Microwave Background (CMB)
polarization by the BICEP2 experiment, if interpreted as evidence for a
primordial gravitational wave background, has enormous ramifications for
cosmology and physics. It is crucial to test this hypothesis with independent
measurements. A gravitational wave background leads to B-modes in galaxy shape
correlations (shear) both through lensing and tidal alignment effects. Since
the systematics and foregrounds of galaxy shapes and CMB polarization are
entirely different, a detection of a cross-correlation between the two
observables would provide conclusive proof for the existence of a primordial
gravitational wave background. We find that upcoming weak lensing surveys will
be able to detect the cross-correlation between B-modes of the CMB and galaxy
shapes. However, this detection is not sufficient to confirm or falsify the
hypothesis of a primordial origin for CMB B-mode polarization.
