  We compute the effects of a stochastic background of gravitational waves on
multiply imaged systems or on weak lensing. There are two possible observable
effects, a static relative deflection of images or shear, and an induced time
dependent shift or proper motion. We evaluate the rms magnitude of these
effects for a COBE normalized, scale-invariant spectrum, which is an upper
limit on spectra produced by inflation. Previous work has shown that
large-scale structure may cause a relative deflection large enough to affect
observations, but we find that the corresponding effect of gravity waves is
smaller by $\sim 10^4$ and so cannot be observed. This results from the
oscillation in time as well as the redshifting of the amplitude of gravity
waves. We estimate the magnitude of the proper motion induced by deflection of
light due to large-scale structure, and find it to be $\sim 10^{-8}$ arcsec per
year. This corresponds to $\sim 50$ km/s at cosmological distances, which is
quite small compared to typical peculiar velocities. The COBE normalized
gravity wave spectrum produces motions smaller still by $\sim 10^2$. We
conclude that light deflection due to these cosmological perturbations cannot
produce observable proper motions of lensed images. On the other hand, there
are only a few known observational limits on a stochastic background of gravity
waves at shorter, astrophysical wavelengths. We calculate the expected
magnitudes of the effects of lensing by gravity waves of such wavelengths, and
find that they are too small to yield interesting limits on the energy density
of gravity waves.
