  We investigate the effect of primordial non-Gaussianity on the
cross-correlation between the CMB anisotropies and the 21 cm fluctuations from
the epoch of reionization. We assume an analytic reionization model and an
ionization fraction with $f_{\rm NL}$ induced scale dependent bias. We estimate
the angular power spectrum of the cross-correlation of the CMB and 21 cm. In
order to evaluate the detectability, the signal-to-noise (S/N) ratio for only a
single redshift slice is also calculated for current and future observations,
such as CMB observations by Planck satellite and 21 cm observations by
Omniscope. The existence of the $f_{\rm NL}$ increases the signal of the
cross-correlation at large scales and the amplification does not depend on the
reionization parameters in our reionization model. However the cosmic variance
is significant on such scales and the S/N ratio is suppressed. The obtained S/N
ratio is 2.8 (2.4) for $f_{\rm NL}=10$ (100) in our fiducial reionization
model. Our work suggests in the absence of significant foregrounds and
systematics, the auto-correlations of 21 cm is a better probe of $f_{\rm NL}$
than the cross-correlations (as expected since it depends on $b^2$), while the
cross-correlations contain only one factor of $b$. Nevertheless, it is
interesting to examine the cross-correlations between 21 cm and CMB, as the
signal-to-noise ratio is not negligible and it is more likely we can rid
ourselves of systematics and foregrounds that are common to both CMB and 21 cm
experiments than completely clean 21 cm of all of the possible foregrounds and
systematics in large scales.
