  We consider the polarization of 21cm line radiation from the epoch of
reionization due to both intrinsically polarized emission and secondary
mechanisms. We argue that Thomson scattering of the 21cm quadrupole by the
reionized universe is likely to produce the largest effect. The 21cm quadrupole
is sourced by baryonic density fluctuations and the fluctuations in the
ionization fraction due to discrete \ion{H}{2} regions. Since Thomson
scattering produces only E-type polarization and is achromatic, its unique
fingerprint can in principle be separated from foregrounds associated with
polarized synchrotron emission which should not be correlated with the cosmic
signal. We estimate that Poisson fluctuations of \ion{H}{2} regions at the end
of reionization ($z_R \sim 6$--20) produce a brightness
temperature-polarization cross-correlation signal of $\sim 0.1 - 0.3 {mK}$ on
angular scales of tens of arcminutes. This cross-correlation signal is within
the instrument sensitivities of the future {\it Square Kilometer Array} (SKA)
and close to the sensitivities of the forthcoming {\it Mileura Widefield Array}
(MWA) and {\it Low Frequency Array} (LOFAR).
