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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 $Δz_e$ $\sim$ $0.05$ $-$ $0.5$ 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$α$ 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.