  The observed magnetic field of microgauss strength in clusters of galaxies
should induce the Faraday rotation effect on the linearly polarized cosmic
microwave background (CMB) radiation when the CMB radiation propagates through
a cluster at low redshift. Employing the Press-Schechter prescription for the
cluster abundance under the cold dark matter (CDM) scenario and a plausible
isothermal $\beta$-model for the gas distribution, we compute angular power
spectra of the CMB polarization fields including the Faraday rotation mixing
effect under the simple assumption of uniform magnetic field configuration
across a cluster. As a result, we find that a parity-odd B-type polarization
pattern is statistically generated on the observed sky, even when the primary
polarization only contains the parity-even E-mode component, such as in the
case of pure scalar perturbations. The generated B-type polarization has a peak
with amplitude of $\sim0.1 \mu{\rm K}(B_0/0.1 \mu{\rm G})(\nu_0/10 {\rm
GHz})^{-2}$ at angular scales of $l\approx 1000$ for the currently favored
adiabatic $\Lambda$CDM model. This result also implies that, if the magnetic
field has a $0.5 \mu{\rm G}$ strength and we observe at lower frequencies such
as $\nu_0\simlt 5 {\rm GHz}$, the secondary signal due to the Faraday rotation
effect could be comparable to the magnitude of the primary polarization. The
frequency dependence of the Faraday rotation can be then used to discriminate
the effect from primary and other secondary signals on the CMB polarizations.
Our results therefore offer a new empirical opportunity to measure or constrain
the intracluster magnetic field in the average sense.
