We study the transmission properties of a one-dimensional array with intersite side-coupled defect and demonstrate that, as the system undergoes sharp Fano resonance, it exhibits geometry-induced vorticity of the energy flux. The optical vortex inverts its handedness at the Fano resonance, revealing a strong link between two phenomena, both being of interference origin. Our approach is quite general and can be applied to a variety of systems; as an example we demonstrate a similar effect in photonic crystal structure.