We propose that the observed small (100 ps) spin relaxation time in graphene is due to resonant scattering by local magnetic moments. At resonances, magnetic moments behave as spin hot spots: the spin-flip scattering rates are as large as the spin-conserving ones, as long as the exchange interaction is greater than the resonance width. Smearing of the resonance peaks by the presence of electron-hole puddles gives quantitative agreement with experiment, for about 1 ppm of local moments. Although magnetic moments can come from a variety of sources, we specifically consider hydrogen adatoms, which are also resonant scatterers. The same mechanism would also work in the presence of a strong local spin-orbit interaction, but this would require heavy adatoms on graphene or a much greater coverage density of light adatoms. To make our mechanism more transparent, we also introduce toy atomic chain models for resonant scattering of electrons in the presence of a local magnetic moment and Rashba spin-orbit interaction.