We investigate the flow patterns created when a liquid drop contacts a reservoir liquid, which has implications on various physicochemical and biochemical reactions including mixing in microfluidic systems. The localized vortical flow spontaneously triggered by the difference of surface tension between the two liquids is studied, which is thus termed the Marangoni vortex. To quantitatively investigate the strength of vortices, we performed particle image velocimetry (PIV) experiments by varying the surface tension difference, the gap of the flow cell, the density and viscosity of the reservoir liquid, and the size of the drop. A scaling law that balances the interfacial energy of the system with the kinetic energy of the vortical flows allows us to understand the functional dependence of the Marangoni vortex strength on various experimental parameters.