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Optical methods for droplet manipulation are attractive because they offer dynamic control without on-chip structures; however, forces from optical tweezers tend to be in the pN range. We demonstrate the trapping of oil-in-water droplets on a focused laser beam via using Marangoni optofluidic tweezers (MOT). MOR exploits Marangoni flow generated by a laser-induced temperature singularity at the oil-water interface. The asymmetry of the flow aligns the droplet centroid to the laser, at which point the flow becomes symmetric and stabilizes the droplet. MOT forces are several orders of magnitude stronger (μN) than optical tweezers, evidenced by the manipulation of 20-1000 μm oil dropletsat speeds >; 1 mm mm/s. The flows within the droplet can also be used for mixing and particle collection within the drop, and adjacent secondary vortices can merge droplets. The self-alignment mechanism is supported by CFD simulations, and experimental data.