  We describe polarization of the Sunyaev-Zel'dovich (SZ) effect associated
with electron pressure anisotropy likely present in the intracluster medium
(ICM). The ICM is an astrophysical example of a weakly collisional plasma where
the Larmor frequencies of charged particles greatly exceed their collision
frequencies. This permits formation of pressure anisotropies, driven by
evolving magnetic fields via adiabatic invariance, or by heat fluxes. SZ
polarization arises in the process of Compton scattering of the cosmic
microwave background (CMB) photons off the thermal ICM electrons due to the
difference in the characteristic thermal velocities of the electrons along two
mutually orthogonal directions in the sky plane. The signal scales linearly
with the optical depth of the region containing large-scale correlated
anisotropy, and with the degree of anisotropy itself. It has the same spectral
dependence as the polarization induced by cluster motion with respect to the
CMB frame (kinematic SZ effect polarization), but can be distinguished by its
spatial pattern. { For the illustrative case of a galaxy cluster with a cold
front, where electron transport is mediated by Coulomb collisions, we estimate
the CMB polarization degree at the level of 10$^{-8}$ ($\sim 10$ nK). An
increase of the effective electron collisionality due to plasma instabilities
will reduce the effect. Such polarization, therefore, may be an independent
probe of the electron collisionality in the ICM, which is one of the key
properties of a high-$\beta$ weakly collisional plasma from the point of view
of both astrophysics and plasma theory.
