We have experimentally observed an eddy current of exciton polaritons arising in a cylindrical GaAs/AlGaAs pillar microcavity under the nonresonant optical pumping. The polariton current manifests itself in a Mach-Zehnder interferometry image as a characteristic spiral that occurs due to the interference of the light emitted by an exciton-polariton condensate with a reference spherical wave. We have experimentally observed the condensates with the topological charges m=+1,m=-1, and m=-2. The interference pattern corresponding to the m=-2 current represents the twin spiral emerging from the center of the micropillar. The switching between the current modes with different topological charges is achieved by a weak displacement of the pump spot.