We observe significant orbital angular momentum (OAM)-helicity-dependent centroid shifts in the Fraunhofer patterns for the far-field diffraction of optical vortex beams passing through a thin single wire, thus suggesting the orbital Hall effect (OHE) of light in diffraction. Based on the OHE with a thin cross wire, we further experimentally develop a compact and robust alignment-free method to measure the OAM states of light. These findings indicate that not only does the OHE of light offer insights into vortex diffraction with broken rotational symmetry, it may also provide a reliable and efficient way to simplify the vortex measurement for waves of different natures.