Collisionless shocks are efficient particle accelerators. While ion acceleration by shocks has been intensively studied using spacecraft data and numerical models, the main focus has been on the case of a steady upstream. In the steady upstream case, it has been shown that quasi-parallel shocks are much more efficient ion accelerators than quasi-perpendicular shocks. However, the solar wind is in general highly dynamic, containing current sheets which correspond to a magnetic shear. In this study we use a local 2.5D hybrid particle-in-cell (particle ions, fluid electrons) model to study how the ion acceleration of quasi-perpendicular shocks is affected when the upstream contains highly sheared tangential discontinuities. We show that, even in the absence of foreshock transients, the current sheets can cause a significant increase in the flux of high-energy ions. The acceleration can be explained by the following simple model. When the upstream TD is close to the shock, the shock-reflected ions can cross it during the upstream part of their gyro–motion. After crossing the TD, the large magnetic shear, corresponding to a sign change of the magnetic field direction, results in a meandering ion trajectory. This motion takes the ion further upstream, where it is further energized by the upstream convection electric field. The net effect of this process is a local ion acceleration efficiency of a few %, as quantified as the fraction of energy (in the downstream and in the downstream frame) that is carried by ions with energies larger than 10 times the upstream bulk kinetic energy. This is comparable to the efficiency of quasi-parallel shocks in the case of a steady upstream. Such discontinuities can therefore be an important source of energetic ions at quasi-perpendicular shocks, even if no foreshock transient is formed.