Exoplanet searches have discovered a large number of "hot Jupiters"–high-mass planets orbiting very close to their parent stars in nearly circular orbits. A number of these planets are sufficiently massive and close-in to be significantly affected by tidal dissipation in the parent star, to a degree parameterized by the tidal quality factor Q*. This process speeds up their star's rotation rate while reducing the planet's semimajor axis. In this paper, we investigate the tidal destruction of hot Jupiters. Because the orbital angular momenta of these planets are a significant fraction of their star's rotational angular momenta, they spin up their stars significantly while spiraling to their deaths. Using the Monte Carlo simulation, we predict that for Q*= 106, 3.9x10–6 of stars with the Kepler Target Catalog's mass distribution should have a rotation period shorter than 1/3 day (8 hr) due to accreting a planet. Exoplanet surveys such as SuperWASP, HATnet, HATsouth, and KELT have already produced light curves of millions of stars. These two facts suggest that it may be possible to search for tidally destroyed planets by looking for stars with extremely short rotational periods, then looking for remnant planet cores around those candidates, anomalies in the metal distribution, or other signatures of the recent accretion of the planet.