  Weak gravitational lensing by foreground density perturbations generates a
gradient mode in the shear of background images. In contrast, cosmological
tensor perturbations induce a non-zero curl mode associated with image
rotations. In this note, we study the lensing signatures of both primordial
gravitational waves from inflation and second-order gravitational waves
generated from the observed spectrum of primordial density fluctuations. We
derive the curl mode for galaxy lensing surveys at redshifts of 1 to 3 and for
lensing of the cosmic microwave background (CMB) at a redshift of 1100. We find
that the curl mode angular power spectrum associated with secondary tensor
modes for galaxy lensing surveys dominates over the corresponding signal
generated by primary gravitational waves from inflation. However, both tensor
contributions to the shear curl mode spectrum are below the projected noise
levels of upcoming galaxy and CMB lensing surveys and therefore are unlikely to
be detectable.
