The Arctic halocline is generally stable to the development of double-diffusive and dynamic instabilities – the two major sources of small-scale mixing in the mid-latitude oceans. Despite this, observations show the abundance of double-diffusive staircases in the Arctic Ocean, which suggests the presence of some destabilizing process facilitating the transition from smooth-gradient to layered stratification. Recent studies have shown that an instability can develop in such circumstances if weak static shear is present even when the flow is dynamically and diffusively stable. However, the impact of oscillating shear, associated with the presence of internal gravity waves, has not yet been addressed for the diffusive case. Through two-dimensional simulations of diffusive convection, we have investigated the impact of the magnitude and frequency of externally forced oscillatory shear on the thermohaline-shear instability. Simulations with stochastic shear – characterized by a continuous spectrum of frequencies from inertial to buoyancy – indicate that thermohaline layering does occur due to the presence of destabilizing modes (oscillations of near the buoyancy frequency). These simulations show that such layers appear as well-defined steps in the temperature and salinity profiles. Thus, the thermohaline-shear instability is a plausible mechanism for staircase formation in the Arctic and merits substantial future study.