Reports of emergent conductivity, superconductivity and magnetism have helped to fuel intense interest in the rich physics and technological potential of complex-oxide interfaces. Here we employ magnetic force microscopy to search for room-temperature magnetism in the well-studied LaAlO3/SrTiO3 system. Using electrical top gating to control the electron density at the oxide interface, we directly observe the emergence of an in-plane ferromagnetic phase as electrons are depleted from the interface. Itinerant electrons that are reintroduced into the interface align antiferromagnetically with the magnetization at first screening and then destabilizing it as the conductive regime is approached. Repeated cycling of the gate voltage results in new, uncorrelated magnetic patterns. This newfound control over emergent magnetism at the interface between two non-magnetic oxides portends a number of important technological applications.