  The Red-Sequence Cluster Survey (RCS) provides a large and deep photometric
catalog of galaxies in the $z'$ and $R_c$ bands for ~90 square degrees of sky,
and supplemental $V$ and $B$ data have been obtained for 33.6 deg$^{2}$. We
compile a photometric redshift catalog from these 4-band data by utilizing the
empirical quadratic polynomial photometric redshift fitting technique in
combination with CNOC2 and GOODS/HDF-N redshift data. The training set includes
4924 spectral redshifts. The resulting catalog contains more than one million
galaxies with photometric redshifts $< 1.5$ and $R_c < 24$, giving an rms
scatter $\sigma(\Delta{z}) < 0.06$ within the redshift range $0.2 < z < 0.5$
and $\sigma(\Delta{z}) < 0.11$ for galaxies at $0.0 < z < 1.5$. We describe the
empirical quadratic polynomial photometric redshift fitting technique which we
use to determine the relation between redshift and photometry. A kd-tree
algorithm is used to divide up our sample to improve the accuracy of our
catalog. We also present a method for estimating the photometric redshift error
for individual galaxies. We show that the redshift distribution of our sample
is in excellent agreement with smaller and much deeper photometric and
spectroscopic redshift surveys.
