  We study the signal in the Cosmic Microwave Background (CMB) polarization
anisotropy resulting from patchy reionization. It is well known that the
primordial polarization of the CMB is very sensitive to the details of
reionization. Combining a semi-analytic model of galaxy formation, in which the
optical depth to the reionization epoch is in the range 0.014 to 0.048, with a
high resolution N-body simulation we find that reionization generates a peak
with amplitude 0.05~0.15 \mu K at large angular scales. The position of this
peak reveals the size of the horizon at reionization, whilst its amplitude is a
measure of the optical depth to reionization. On small scales, ionized patches
prior to full reionization create a second order polarization signal due to the
coupling of the free electron density fluctuation with the quadrupole moment of
the temperature anisotropy. Careful study reveals that the coupling generates
the same power spectra for electric and magnetic modes, whose amplitudes of
polarization anisotropies from this process are predicted to be ~10nK. The
amplitude depends strongly on the total baryon density $\Omega_b$ and on the
spatial correlations of the free electron density in the ionized regions, and
weakly on the fraction of ionizing photons able to escape their source galaxy,
$f_{esc}$. The first- and second-order signals are therefore sensitive to the
details of how the reionization occurred. Detection of these signals will place
important constraints on the reionization history of the Universe.
