  As is known, resonant scattering can distort the surface-brightness profiles
of clusters of galaxies in X-ray lines. We demonstrate that the scattered line
emission should be polarized and possibly detectable with near-future X-ray
polarimeters. Spectrally-resolved mapping of a galaxy cluster in polarized
X-rays could provide valuable independent information on the physical
conditions, in particular element abundances and the characteristic velocity of
small-scale turbulent motions, in the intracluster gas. The expected degree of
polarization is of the order of 10% for richest regular clusters (e.g. Coma)
and clusters whose X-ray emission is dominated by a central cooling flow (e.g.
Perseus or M87/Virgo).
