The wavelength dependence of atmospheric refraction causes differential chromatic refraction (DCR), whereby objects imaged at different optical/UV wavelengths are observed at slightly different positions in the plane of the detector. Strong spectral features induce changes in the effective wavelengths of broad-band filters that are capable of producing significant positional offsets with respect to standard DCR corrections. We examine such offsets for broad-emission-line (type 1) quasars from the Sloan Digital Sky Survey (SDSS) spanning 0<z<5 and an airmass range of 1.0 to 1.8. These offsets are in good agreement with those predicted by convolving a composite quasar spectrum with the SDSS bandpasses as a function of redshift and airmass. This astrometric information can be used to break degeneracies in photometric redshifts of quasars (or other emission-line sources) and, for extreme cases, may be suitable for determining astrometric redshifts. On the SDSSs southern equatorial stripe, where it is possible to average many multi-epoch measurements, more than 60% of quasars have emission-line-induced astrometric offsets larger than the SDSSs relative astrometric errors of 25-35 mas. Folding these astrometric offsets into photometric redshift estimates yields an improvement of 9% within Delta z+/-0.1. Future multi-epoch synoptic surveys such as LSST and Pan-STARRS could benefit from intentionally making ~10 observations at relatively high airmass (AM~1.4) in order to improve their photometric redshifts for quasars.