A single vortex is excited into nano-size Pb superconducting island structures by a local current injection from a probe tip of a scanning tunneling microscope. For the excitation, a sufficient amount and duration of the pulsed current are required. Injecting the current at peripheral sites is more effective than the center for the vortex excitation. Time-dependent Ginzburg-Landau calculations suggest that a current-induced normal-state area, which can be nucleated by the tunneling current exceeding the critical current and expanded by the Joule heating, reduces the required magnetic field for the vortex penetration and excites a vortex into the islands.