The TESS spacecraft obtained high-precision space-based time-series photometry of nearly the entire sky during its Prime Mission, allowing for a large-scale study of stellar variability that is not sensitive to the diurnal limitation of ground-based surveys. We present the TESS-Stellar Variability Catalog (TESS-SVC), which includes ~84,000 stars that exhibit significant photometric variability on timescales of 0.01-13 days. The TESS-SVC includes a broad range of periodic variable stars (rotation, pulsation, eclipsing binaries, etc.) that were selected based on a photometric periodogram analysis of their 2-min cadence light curves. The TESS-SVC is now available as a HLSP on MAST that includes tabulated information about the periodic variability measured and stellar properties extracted from the TESS Input Catalog, in addition to a summary figure for each star that shows the resultant periodogram and best-fit curve to the stellar variability. The catalog will continue to be updated as new TESS data becomes available, and it will later include stars that exhibit photometric variability on timescales longer than 13 days. I will discuss the characteristics of the stars in the TESS-SVC, which will serve as a valuable resource to the stellar astrophysics and exoplanet communities. The variability catalog will aid in 1) studying the characteristics of periodic variable stars; 2) understanding interactions between host star variability and planetary atmospheres; and 3) identifying exoplanets that are actually false positives caused by stellar variability.