ABSTRACT We present the first observational evidence that light propagating near a rotating black hole is twisted in phase and carries orbital angular momentum (OAM). This physical observable allows a direct measurement of the rotation of the black hole. We extracted the OAM spectra from the radio intensity data collected by the Event Horizon Telescope from around the black hole M87* by using wavefront reconstruction and phase recovery techniques and from the visibility amplitude and phase maps. This method is robust and complementary to black hole shadow circularity analyses. It shows that the M87* rotates clockwise with an estimated rotation parameter a = 0.90 ± 0.05 with an $∼ 95{{\ \rm per\ cent}}$ confidence level (c.l.) and an inclination i = 17° ± 2°, equivalent to a magnetic arrested disc with an inclination i = 163° ± 2°. From our analysis, we conclude that, within a 6σ c.l., the M87* is rotating.