  We predict that a photon condensate inside a dye-filled microcavity forms
long-lived spatial structures that resemble vortices when incoherently excited
by a focused pump orbiting around the cavity axis. The finely structured
density of the condensates have a discrete rotational symmetry that is
controlled by the orbital frequency of the pump spot and is phase-coherent over
its full spatial extent despite the absence of any effective photon-photon
interactions.
