The dispersion measure of extragalactic radio transients, such as of recently discovered Fast Radio Burst FRB150418, can be used to measure the column density of free electrons in the intergalactic medium. The same electrons also scatter the Cosmic Microwave Background (CMB) photons, affecting precision measurements of cosmological parameters. We explore the connection between the dispersion measure of radio transients existing during the Epoch of Reionization (EoR) and the total optical depth for the CMB, $\tau CMB$, showing that the existence of such transients would provide a new sensitive probe of $\tau CMB$. As an example, we consider the population of FRBs. Assuming they exist during the EoR, we show that: (i) such sources can probe the reionization history by measuring $\tau CMB$ to sub-percent accuracy, and (ii) they can be detected with high significance by an instrument such as the Square Kilometer Array.