Abstract Strike‐slip faults act as landscape change agents, offsetting rivers, driving river capture, and generating hillslope responses. In this study, inspired by the hyperarid Atacama Fault System in Chile, we use numerical models to investigate how landscapes that experience oscillatory dry and humid periods respond to strike‐slip faulting at variable slip rates. Our results show that riverbed aggradation from hillslope sediment flux during dry periods delays stream capture, increases deflection angles of fault‐crossing channels, and produces highly perturbed longitudinal river profiles. In some cases, these phenomena, as well as the thickness of aggraded sediment, are slip‐rate dependent. Lags in capture timing and/or fully missed captures that occur in landscapes with climatic oscillation have a profound impact on the long‐term evolution of strike‐slip landscapes. Our work also highlights the importance of hillslope contributions to landscape modification in arid and semi‐arid settings with ephemeral rivers.