Context. Planet formation is expected to take place in the first million years of a planetary system through various processes, which remain to be tested through observations. Aims. With the recent discovery, using ALMA, of two gaseous spiral arms inside the ∼120 au cavity and connected to dusty spirals, the famous protoplanetary disk around AB Aurigae presents a strong incentive for investigating the mechanisms that lead to giant planet formation. A candidate protoplanet located inside a spiral arm has already been claimed in an earlier study based on the same ALMA data. Methods. We used SPHERE at the Very Large Telescope to perform near-infrared high-contrast imaging of AB Aur in polarized and unpolarized light in order to study the morphology of the disk and search for signs of planet formation. Results. SPHERE has delivered the deepest images ever obtained for AB Aur in scattered light. Among the many structures that are yet to be understood, we identified not only the inner spiral arms, but we also resolved a feature in the form of a twist in the eastern spiral at a separation of about 30 au. The twist of the spiral is perfectly reproduced with a planet-driven density wave model when projection effects are accounted for. We measured an azimuthal displacement with respect to the counterpart of this feature in the ALMA data, which is consistent with Keplerian motion on a 4 yr baseline. Another point sxce is detected near the edge of the inner ring, which is likely the result of scattering as opposed to the direct emission from a planet photosphere. We tentatively derived mass constraints for these two features. Conclusions. The twist and its apparent orbital motion could well be the first direct evidence of a connection between a protoplanet candidate and its manifestation as a spiral imprinted in the gas and dust distributions.