  We describe the effects of weak gravitational lensing by cosmological large
scale structure on the diffuse emission of 21 centimeter radiation from neutral
hydrogen at high redshifts during the era of reionization. The ability to
observe radial information through the frequency, and thus three-dimensional
regions of the background radiation at different redshifts, suggests that 21 cm
studies may provide a useful context for studying weak lensing effects. We
focus on the gravitational lensing effects on both the angular power spectra
and the intrinsic, three-dimensional power spectra. We present a new approach
for calculating the weak lensing signature based on integrating differential
Fourier-space shells of the deflection field and approximating the
magnification matrix. This method is applied to reionization models of the 21
cm spectra up to small angular scales over a range in redshift. The effect on
the angular power spectrum is typically < 1% on small angular scales, and very
small on scales corresponding to the feature imprinted by reionization bubbles,
due to the near-scale invariance of the angular power spectrum of the 21 cm
signal on these scales. We describe the expected effect of weak lensing on
three-dimensional 21 cm power spectra, and show that lensing creates aspherical
perturbations to the intrinsic power spectrum which depend on the polar angle
of the wavevector. The effect on the 3D power spectrum is < 1% on scales k <
0.1 h/Mpc, but can be > 1% for highly inclined modes for k > 1 h/Mpc. The
angular variation of the lensing effect on these scales is well described by a
quartic polynomial in the cosine of the polar angle. The detection of the
gravitational lensing effects on 21 cm power spectra will require very
sensitive, high resolution observations by future low-frequency radio arrays.
