  Scattering of the cosmic microwave background (CMB) in clusters of galaxies
polarizes the radiation. We explore several polarization components which have
their origin in the kinematic quadrupole moments induced by the motion of the
scattering electrons, either directed or random. Polarization levels and
patterns are determined in a cluster simulated by the hydrodynamical Enzo code.
We find that polarization signals can be as high as $\sim 1 \mu$K, a level that
may be detectable by upcoming CMB experiments.
