Precise measurements of eclipsing binary parameters and statistical studies of young clusters have suggested that some magnetically active low-mass dwarfs possess radii inflated by ~5%-15% relative to theoretical expectations. If true, this effect should be pronounced in young open clusters, due to the rapid rotation and strong magnetic activity of their most extreme members. We explore this possibility by determining empirical radii for 83 members of the nearby Pleiades open cluster, using spectral energy distribution fitting to establish F_bol_ with a typical accuracy of ~3% together with color and spectro-photometric indices to determine T_eff_. We find several Pleiades members with radii inflated above radius-T_eff_ models from state-of-the-art calculations, and apparent dispersions in radii for the K-dwarfs of the cluster. Moreover, we demonstrate that this putative radius inflation correlates strongly with rotation rate, consistent with inflation of young stars by magnetic activity and/or starspots. We argue that this signal is not a consequence of starspot-induced color anomalies, binarity, or depth effects in the cluster, employing Gaia DR1 distances as a check. Finally, we consider the lithium abundances of these stars, demonstrating a triple correlation between rotation rate, radius inflation, and enhanced lithium abundance. Our result-already significant to ~99.99% confidence-provides strong support for a magnetic origin of the inflated radii and lithium dispersion observed in young, low-mass stars.