Despite its biogenic and astrochemical importance, sulfur (S), the 10th most abundant element in the interstellar medium (ISM) with a total abundance of S/H ≈ 2.2 × 10−5, largely remains undetected in molecular clouds. Even in the diffuse ISM where S was previously often believed to be fully in the gas phase, in recent years, observational evidence has suggested that S may also be appreciably depleted from the gas. What might be the dominant S reservoir in the ISM remains unknown. Solid sulfides like MgS, FeS, and SiS2 are excluded as major S reservoirs due to the nondetection of their expected infrared spectral bands in the ISM. In this work, we explore the potential role of sulfurated polycyclic aromatic hydrocarbon (PAH) molecules—PAHs with sulfur heterocycles (PASHs)—as a sink for the missing S. Utilizing density function theory, we compute the vibrational spectra of 18 representative PASH molecules. It is found that these molecules exhibit a prominent C–S stretching band at ∼10 μm and two relatively weak C–S deformation bands at 15 and 25 μm that are not mixed with the nominal PAH bands at 6.2, 7.7, 8.6, 11.3, and 12.7 μm. If several parts per million of S (relative to H) are locked up in PAHs, the 10 μm C–S band would be detectable by Spitzer and the James Webb Space Telescope (JWST). To quantitatively explore the amount of S/H depleted in PASHs, a detailed comparison of the infrared emission spectra of PASHs with the Spitzer and JWST observations is needed.