Current estimates place the ages of the inner Saturnian satellites (Mimas, Enceladus, Tethys, Dione, and Rhea) between 4.5 Gyr and 100 Myr. These estimates are based on impact crater measurements and dynamical simulations, both of which have uncertainties. Models of satellite evolution are inherently simplified and rely on uncertain or unknown parameters, which are often difficult to verify, whereas the interpretations of crater densities depend on the source populations of impactors, which are not well‐constrained in the outer solar system. We investigate the cratering history of Tethys, mapping the population of small impact craters, to determine the roles that planetocentric, heliocentric, or other impact debris play in its cratering record. To map the surface of Tethys, we chose five regions that were located in geographically distinct areas and had high‐resolution (~150 m/pix) image coverage by the Cassini ISS camera. We studied all craters that had at least 7 pixels across but mapped down to 5 pixels for completeness in the crater counts. We observe an abundance of small craters (D < 3 km) in the oldest region; this does not appear to be due to secondary cratering effects from the Odysseus impact basin. Fitting the production functions from Zahnle et al. (2003, https://doi.org/10.1016/S0019‐1035(03)00048‐4), we find that neither their Case A nor Case B scenarios align with the observed cratering record at Tethys. We conclude that in addition to the standard outer solar system impactor populations, there is a Saturn‐centric impactor source that is cratering Tethys.