  Differential Chromatic Refraction (DCR) is caused by the wavelength
dependence of our atmosphere's refractive index, which shifts the apparent
positions of stars and galaxies and distorts their shapes depending on their
spectral energy distributions (SEDs). While this effect is typically mitigated
and corrected for in imaging observations, we investigate how DCR can instead
be used to our advantage to infer the redshifts of supernovae from multi-band,
time-series imaging data. We simulate Type Ia supernovae (SNe Ia) in the
proposed Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) Deep
Drilling Field (DDF), and evaluate astrometric redshifts. We find that the
redshift accuracy improves dramatically with the statistical quality of the
astrometric measurements as well as with the accuracy of the astrometric
solution. For a conservative choice of a 5-mas systematic uncertainty floor, we
find that our redshift estimation is accurate at $z < 0.6$. We then combine our
astrometric redshifts with both host galaxy photometric redshifts and
supernovae photometric (light-curve) redshifts and show that this considerably
improves the overall redshift estimates. These astrometric redshifts will be
valuable especially since Rubin will discover a vast number of supernovae for
which we will not be able to obtain spectroscopic redshifts.
