We propose an innovative method for measuring the neutral hydrogen (HI) content of an optically-selected spectroscopic sample of galaxies through cross-correlation with HI intensity mapping measurements. We show that the HI-galaxy cross-power spectrum contains an additive shot noise term which scales with the average HI brightness temperature of the optically-selected galaxies, allowing constraints to be placed on the average HI mass per galaxy. This approach can estimate the HI content of populations too faint to directly observe through their 21cm emission over a wide range of redshifts. This cross-correlation, as a function of optical luminosity or colour, can be used to derive HI-scaling relations. We demonstrate that this signal will be detectable by cross-correlating upcoming Australian SKA Pathfinder (ASKAP) observations with existing optically-selected samples. We also use semi-analytic simulations to verify that the HI mass can be successfully recovered by our technique in the range M_HI > 10^8 M_solar, in a manner independent of the underlying power spectrum shape. We conclude that this method is a powerful tool to study galaxy evolution, which only requires a single intensity mapping dataset to infer complementary HI gas information from existing optical and infra-red observations.
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