We present the first numerical simulations of a thin accretion disk around a Reissner-Nordstr & ouml;m (RN) naked singularity (NkS; a charged point mass). The gravity of the RN NkS is modeled with a pseudo-Newtonian potential that reproduces exactly the radial dependence of the RN Keplerian orbital frequency; in particular, orbital angular velocity vanishes at the zero gravity radius and has a maximum at 4/3 of that radius. Angular momentum is transported outward by viscous stresses only outside the location of this maximum. Nonetheless, even at that radius, accretion proceeds at higher latitudes, the disk having thickened there owing to excess pressure. The accretion stops at a certain distance away from the singularity, with the material accumulating in a toroidal structure close to the zero-gravity sphere. The shape of the structure obtained in our simulations is reminiscent of fluid figures of equilibrium analytically derived in full general relativity for the RN singularity. The presence of a rotating ring, such as the one found in our simulations, could be an observational signature of an NkS. For charge-to-mass ratios close to but larger than unity, the inner edge of the quasi-toroidal inner accretion structure would be located well within the Schwarzschild marginally stable orbit (ISCO), and the maximum orbital frequency in thin accretion disks would be much higher than the Schwarzschild ISCO frequency.