The current study aims to further comprehend the influence of inlet distortion during flight on the propagation of rotating detonation waves (RDW) in annular rotating detonation engines (RDE). The inlet flow parameters play an important role in the operation characteristics of rotating detonation. However, the dynamic behavior of the detonation wave corresponding to non-uniform inflow condition remains unclear. In this study, inlet distortion is simplified as a sinusoidal-typed non-uniform total pressure inlet flow condition. Through two-dimensional numerical simulations, we analyze the influence of non-uniform total pressure distribution on the dynamic propagation of the rotating detonation wave. This paper examines the effect of the inlet total pressure disturbance amplitude A ranging from 0.0 to 0.7 and the inlet injection area ratio S ranging from 0.2 to 8.8 on the rotating detonation wave propagation process. The findings indicate that RDWs could adjust to a wide range of distorted inlet air flow with disturbance amplitude A from 0.0 to 0.7. And as the inlet injection area ratio S decreases, the peak pressure of the detonation wave increases. The response to non-uniform total pressure is consistent between different injection area ratio cases.