The ultrafast nuclear dynamics of the acetylene cation C2H2+ following photoionization of the neutral molecule is investigated using an extreme-ultraviolet pump/infrared probe setup. The observed modulation of the C2H+ fragment ion yield with pump-probe delay is related to structural changes induced by the extreme-ultraviolet pump pulse taking place on the femtosecond timescale. High-level simulations suggest that the trans-bending and C-C bond stretching motion of the C2H2+ cation govern the observed interaction with the infrared pulse. Depending on the molecular configuration at arrival of the infrared pulse, it either transfers population to higher-lying states or to the C2H2+ ground state, thereby enhancing or lowering the C2H+ yield. Our ultrafast pump-probe scheme can thus be used to track excited state nuclear dynamics with a resolution of a few femtoseconds, leading the way to studying fast dynamics also in larger hydrocarbon molecules.