Approximately 33,000 valence-precise, ordered, inorganic compounds tabulated in the Inorganic Crystal Structures Database have been screened for their potential as photovoltaic (PV) absorbers. This has been accomplished through the use of proxies for charge carrier mobilities and optical absorption properties from electronic structure calculations, in addition to constraints on thermodynamic stability. Preliminary screening of computed properties tabulated in the Materials Project database, with subsequent high(er)-fidelity electronic structure calculations of optical properties and band gap corrections indicate ≈200 known compounds on or near the convex hull which exhibit Spectroscopic Limited Maximum Efficiency (SLME) in excess of 25 % for a 500 nm thin film, in addition to possessing low effective masses for both electrons and holes. Among the predicted high-performers are nearly all the known commercial inorganic thin-film PV materials as well as several previously unexplored candidates. The new candidates are drawn from a diversity of chemical and structural families, including many chalcogenides and pnictides as well as anti-perovskites, skutterudites, and semiconducting intermetallics. Carrier effective masses, SLME, corrected band gaps, and other relevant information for ≈800 compounds are made available for further analyses via the Materials Project MPContribs Framework. Supporting Information Computed parameters for the ≈800 candidate phases, and further methodological details. Additionally, structured digital datasets of computed absorption spectra, densities of states, SLME, effective masses, and a list of all ≈33,000 phases which were screened are available at https://materialsproject.org/mpcontribs/ScreeningInorganicPV.