  We present an empirical algorithm for obtaining photometric redshifts of
quasars using 5-band Sloan Digital Sky Survey (SDSS) photometry. Our algorithm
generates an empirical model of the quasar color-redshift relation, compares
the colors of a quasar candidate with this model, and calculates possible
photometric redshifts. Using the 3814 quasars of the SDSS Early Data Release
Quasar Catalog to generate a median color-redshift relation as a function of
redshift we find that, for this same sample, 83% of our predicted redshifts are
correct to within |Delta z|<0.3. The algorithm also determines the probability
that the redshift is correct, allowing for even more robust photometric
redshift determination for smaller, more restricted samples. We apply this
technique to a set of 8740 quasar candidates selected by the final version of
the SDSS quasar-selection algorithm. The photometric redshifts assigned to
non-quasars are restricted to a few well-defined values. In addition, 90% of
the objects with spectra that have photometric redshifts between 0.8 and 2.2
are quasars with accurate (|Delta z|<0.3) photometric redshifts. Many of these
quasars lie in a single region of color space; judicious application of
color-cuts can effectively select quasars with accurate photometric redshifts
from the SDSS database. When the SDSS is complete, this technique will allow
the determination of photometric redshifts for ~10^6 faint SDSS quasar
candidates, enabling advances in our knowledge of the quasar luminosity
function, gravitational lensing of quasars, and correlations among quasars and
between galaxies.
