The Kerr-Newman solution to the Einstein-Maxwell equations in General Relativity describes the behavior of a charged, spinning black hole. We show that an appropriate modification of this result can be interpreted as a classical model for the electron as a point charge with the correct rest mass, angular momentum and magnetic moment. The Coulomb singularity causes a warping of spacetime around the point charge and a resulting polarization of the vacuum analogous to what happens, according to Hawking, in the vicinity of a black hole. The rest-energy and angular momentum of the electron can be attributed to its associated electromagnetic field. This provides a classical model mirroring essential features of Dirac's relativistic quantum theory of the electron, including the g-factor of 2.