The layered semimetal WTe_2 has recently been found to be a two-dimensional topological insulator (2D TI) when thinned down to a single monolayer, with conducting helical edge channels. We report here that intrinsic superconductivity can be induced in this monolayer 2D TI by mild electrostatic doping, at temperatures below 1 K. The 2D TI-superconductor transition can be easily driven by applying a just a small gate voltage. This discovery offers new possibilities for gate-controlled devices combining superconductivity and topology, and could provide a basis for quantum information schemes based on topological protection.