Graphene is the physical realization of many fundamental concepts and phenomena in solid-state physics. However, in the list of graphene\'s many remarkable properties, superconductivity is notably absent. If it were possible to find a way to induce superconductivity, it could improve the performance and enable more efficient integration of a variety of promising device concepts including nanoscale supeconducting quantum interference devices, single-electron superconductor-quantum dot devices, nanometre-scale superconducting transitstors and cryogenic solid-state coolers. To this end, we explore the possibility of inducing superconductivity in a graphene sheet by doping its surface with alkaline metal adatoms, in a manner analogous to which superconductivity is induced in graphite intercalated compounds (GICs). As for GICs, we find that the electrical characteristics of graphene are sensitive to the species of adatom used. However, contrary to what happens in GICs, Li-covered graphene is superconducting at a much higher temperature with respect to Ca-covered graphene.