Microfluidics has enabled the miniaturization of fluidic systems for various biomedical and industrial applications, including small-scale robotic propulsion. One mechanism for generating propulsive force through microfluidics is by exploiting the solutal Marangoni effect via releasing surfactant on the air-water interface. Surfactants locally reduce the surface tension, which leads to a surface stress that can propel the floating robot, called Marangoni surfer. However, so far the release of the surfactant is not controllable. In this study, we combine microfluidics-based Marangoni propulsion with a novel untethered magnetic pumping mechanism to enhance its controllability. The proposed magnetic micropump capitalizes on the interaction force between two soft magnets, which can generate a pumping force of 4.64mN to actuate a membrane, and achieve a deformation of 450μm. Net flow is achieved using a nozzle/diffuser flow rectifier whose efficacy as a function of the channel geometry is numerically studied. We investigate the flow rate of the pump with regard to the actuation frequency. Finally, we demonstrate its ability to control the motion of the Marangoni surfer.