We consider the polarization of 21 cm line radiation from the epoch of reionization due to both intrinsically polarized emission and secondary mechanisms. We argue that Thomson scattering of the 21 cm quadrupole by the reionized universe is likely to produce the largest effect. The 21 cm quadrupole is sourced by baryonic density fluctuations and the fluctuations in the ionization fraction due to discrete H II regions. Since Thomson scattering produces only E-type polarization and is achromatic, its unique fingerprint could 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 H II regions at the end of reionization (zR ~ 6-20) produce a brightness temperature-polarization cross-correlation signal of ~0.1-0.3?mK on angular scales of tens of arcminutes. This cross-correlation signal is within the instrument sensitivities of the future Square Kilometre Array (SKA) and close to the sensitivities of the forthcoming Mileura Widefield Array (MWA) and Low Frequency Array (LOFAR).
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