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The rotation periods of planet-hosting stars can be used for modeling and mitigating the impact of magnetic activity in radial velocity measurements and can help constrain the high-energy flux environment and space weather of planetary systems. Millions of stars and thousands of planet hosts are observed with the Transiting Exoplanet Survey Satellite (TESS). However, most will only be observed for 27 contiguous days in a year, making it difficult to measure rotation periods with traditional methods. This is especially problematic for field M dwarfs, which are ideal candidates for exoplanet searches, but which tend to have periods in excess of the 27-day observing baseline. We present a new tool, Astraea, for predicting long rotation periods from short-duration light curves combined with stellar parameters from Gaia DR2. Using Astraea, we can predict the rotation periods from Kepler 4-year light curves with 13% uncertainty overall (and a 9% uncertainty for periods > 30 days). By training on 27-day Kepler light curve segments, Astraea can predict rotation periods up to 150 days with 9% uncertainty (5% for periods > 30 days). After training this tool on these 27-day Kepler light curve segments, we applied \texttt{Astraea} to real TESS data. For the 195 stars that were observed by both Kepler and TESS, we were able to predict the rotation periods with 55% uncertainty despite the wild differences in systematics.