  At cosmic recombination, there was supersonic relative motion between baryons
and dark matter, which originated from the baryonic acoustic oscillations in
the early universe. This motion has been considered to have a negligible impact
on the late stage of cosmic reionization because the relative velocity quickly
decreases. However, recent studies have suggested that the recombination in gas
clouds smaller than the local Jeans mass ($\lesssim$ $10^8~M_\odot$) can affect
the reionization history by boosting the number of ultraviolet photons required
for ionizing the intergalactic medium. Motivated by this, we performed a series
of radiation-hydrodynamic simulations to investigate whether the streaming
motion can generate variation in the local reionization history by smoothing
out clumpy small-scale structures and lowering the ionizing photon budget. We
found that the streaming velocity can add a variation of $\Delta z_e$ $\sim$
$0.05$ $-$ $0.5$ in the end-of-reionization redshift, depending on the level of
X-ray preheating and the time evolution of ionizing sources. The variation
tends to be larger when the ionizing efficiency of galaxies decreases toward
later times. Given the long spatial fluctuation scales of the streaming motion
($\gtrsim 100$ Mpc), it can help to explain the Ly$\alpha$ opacity variation
observed from quasars and leave large-scale imprints on the ionization field of
the intergalactic medium during the reionization. The pre-reionization heating
by X-ray sources is another critical factor that can suppress small-scale gas
clumping and can diminish the variation in $z_e$ introduced by the streaming
motion.
