  We introduce a new method for constraining the redshift distribution of a set
of galaxies, using weak gravitational lensing shear. Instead of using observed
shears and redshifts to constrain cosmological parameters, we ask how well the
shears around clusters can constrain the redshifts, assuming fixed cosmological
parameters. This provides a check on photometric redshifts, independent of
source spectral energy distribution properties and therefore free of
confounding factors such as misidentification of spectral breaks. We find that
~40 massive ($\sigma_v=1200$ km/s) cluster lenses are sufficient to determine
the fraction of sources in each of six coarse redshift bins to ~11%, given weak
(20%) priors on the masses of the highest-redshift lenses, tight (5%) priors on
the masses of the lowest-redshift lenses, and only modest (20-50%) priors on
calibration and evolution effects. Additional massive lenses drive down
uncertainties as $N_{lens}^0.5$, but the improvement slows as one is forced to
use lenses further down the mass function. Future large surveys contain enough
clusters to reach 1% precision in the bin fractions if the tight lens mass
priors can be maintained for large samples of lenses. In practice this will be
difficult to achieve, but the method may be valuable as a complement to other
more precise methods because it is based on different physics and therefore has
different systematic errors.
