  The Wilkinson Microwave Anisotropy Probe (WMAP) experiment has detected
reionization at the $5.5 \sigma$ level and has reported a mean optical depth of
$0.088 \pm 0.015$. A powerful probe of reionization is the large-angle $EE$
polarization power spectrum, which is now (since the first five years of data
from WMAP) cosmic variance limited for $2\le l \le6$. Here we consider partial
reionization caused by WIMP dark matter annihilation, and calculate the
expected polarization power spectrum. We compare the dark matter models with a
standard 2-step reionization theory, and examine whether the models may be
distinguished using current, and future CMB observations. We consider dark
matter annihilation at intermediate redshifts ($z<60$) due to halos, as well as
annihilation at higher redshifts due to free particles. In order to study the
effect of high redshift dark matter annihilation on CMB power spectra, it is
essential to include the contribution of residual electrons (left over from
recombination) to the ionization history. Dark matter halos at redshifts $z<60$
influence the low multipoles $l<20$ in the $EE$ power spectrum, while the
annihilation of free particle dark matter at high redshifts $z>100$ mainly
affects multipoles $l>10$.
