  Astrophysical plasmas are typically magnetized, with the Larmor radii of the
charged particles many orders of magnitude smaller than their collisional mean
free paths. The fundamental properties of such plasmas, e.g., conduction and
viscosity, may depend on the instabilities driven by the anisotropy of the
particle distribution functions and operating at scales comparable to the
Larmor scales. We discuss a possibility that the pressure anisotropy of thermal
electrons could produce polarization of thermal bremsstrahlung emission. In
particular, we consider coherent large-scale motions in galaxy clusters to
estimate the level of anisotropy driven by stretching of the magnetic-field
lines by plasma flow and by heat fluxes associated with thermal gradients. Our
estimate of the degree of polarization is $\sim 0.1 \%$ at energies $\gtrsim
kT$. While this value is too low for the forthcoming generation of X-ray
polarimeters, it is potentially an important proxy for the processes taking
place at extremely small scales, which are impossible to resolve spatially. The
absence of the effect at the predicted level may set a lower limit on the
electron collisionality in the ICM. At the same time, the small value of the
effect implies that it does not preclude the use of clusters as (unpolarized)
calibration sources for X-ray polarimeters at this level of accuracy.
