For ongoing studies of the role of rotation in stellar evolution, we require large catalogs of rotation periods for testing and refining gyrochronology. While there is a wealth of data from the Kepler and K2 missions, the Transiting Exoplanet Survey Satellite (TESS) presents both an opportunity and a challenge: despite its all-sky coverage, rotation periods remain hard to detect. We analyzed individual TESS sectors to detect short-period stellar rotation, using only parameters measured from light curves for a robust and unbiased method of evaluating detections. We used random forest classifiers for vetting, trained on a large corpus of period measurements in Kilodegree Extremely Little Telescope data from the Oelkers et al. catalog and using TESS full-frame image light curves generated by eleanor. Finally, using data from the first 26 sectors of TESS, we analyzed 432,704 2 minutes cadence single-sector light curves for FGKM dwarfs. We detected 16,800 periods in individual sector light curves, covering 10,909 distinct targets, and we present a catalog of the median period for each target as measured by a Lomb–Scargle periodogram.