  We study the prospects for measuring the cosmological distribution and
abundance of ionized electrons in the intergalactic medium using galaxy
surveys. Optical light from distant galaxies is subject to Thomson screening by
intervening electrons which distorts the observed galaxy number density,
similar to the effect of weak gravitational lensing magnification. We construct
an estimator for the optical-depth fluctuations from the statistical
anisotropies of galaxy number counts induced by the spatially-varying
optical-depth field. We find near-future galaxy surveys can detect this signal
at signal-to-noise above $\sim10$ depending on galaxy survey specifications. We
highlight various science cases for the measurement of optical-depth
fluctuations.
