  The ubiquitous presence of the Fe line complex in the X-ray spectra of galaxy
clusters offers the possibility of measuring their redshift without resorting
to spectroscopic follow-up observations. In this paper we assess the accuracy
with which the redshift of galaxy clusters can be recovered from an X-ray
spectral analysis of Chandra archival data. This study indicates a strategy to
build large surveys of clusters whose identification and redshift measurement
are both based on X-ray data alone. We apply a blind search for K--shell and
L--shell Fe line complex in X-ray cluster spectra using Chandra archival
observations of galaxy clusters. The Fe line in the ICM spectra can be detected
by simply analyzing the C-statistics variation $\Delta C_{stat}$ as a function
of the redshift parameter. We repeat the measurement under different
conditions, and compare the X-ray derived redshift $z_X$ with the one obtained
by means of optical spectroscopy $z_o$. We explore how a number of priors on
metallicity and luminosity can be effectively used to reduce catastrophic
errors. The $\Delta C_{stat}$ provides the most efficient means for discarding
wrong redshift measures and to estimate the actual error on $z_X$. We identify
a simple and efficient procedure for optimally measuring the redshifts from the
X-ray spectral analysis of clusters of galaxies. When this procedure is applied
to mock catalogs extracted from high sensitivity, wide-area cluster surveys,
such as those proposed with Wide Field X-ray Telescope (WFXT) mission, it is
possible to obtain a complete samples of X-ray clusters with reliable redshift
measurements, thus avoiding time-consuming optical spectroscopic observations.
This methodology will make it possible to trace cosmic growth by studying the
evolution of the cluster mass function directly using X-ray data.
