  We present a template fitting algorithm for determining photometric
redshifts, $z_{\rm phot}$, of candidate high-redshift gamma-ray bursts (GRBs).
Using afterglow photometry, obtained by the Reionization And Transients
InfraRed (RATIR) camera, this algorithm accounts for the intrinsic GRB
afterglow spectral energy distribution (SED), host dust extinction and the
effect of neutral hydrogen (local and cosmological) along the line of sight. We
present the results obtained by this algorithm and RATIR photometry of GRB
130606A, finding a range of best fit solutions $5.6 < z_{\rm phot} < 6.0$ for
models of several host dust extinction laws (none, MW, LMC and SMC), consistent
with spectroscopic measurements of the redshift of this GRB. Using simulated
RATIR photometry, we find our algorithm provides precise measures of $z_{\rm
phot}$ in the ranges $4 < z_{\rm phot} \lesssim 8$ and $9 < z_{\rm phot} < 10$
and can robustly determine when $z_{\rm phot}>4$. Further testing highlights
the required caution in cases of highly dust extincted host galaxies. These
tests also show that our algorithm does not erroneously find $z_{\rm phot} < 4$
when $z_{\rm sim}>4$, thereby minimizing false negatives and allowing us to
rapidly identify all potential high-redshift events.
