Rheotaxis is a common phenomenon in nature that refers to the directed movement of micro-organisms as a result of shear flow. The ability to mimic natural rheotaxis using synthetic micro/nanomotors adds functionality to enable their applications in biomedicine and chemistry. Here, we present a hybrid strategy that can achieve both positive and negative rheotaxis of synthetic bimetallic micromotors by employing a combination of chemical fuel and acoustic force. An acoustofluidic device is developed for the integration of the two propulsion mechanisms. Using acoustic force alone, bimetallic microrods are propelled along the bottom surface in the center of a fluid channel. The leading end of the microrod is always the less dense end, as established in earlier experiments. With chemical fuel (H2O2) alone, the microrods orient themselves with their anode end against the flow when shear flow is present. Numerical simulations confirm that this orientation results from tilting of the microrods relative to the bottom surface of the channel, which is caused by catalytically driven electro-osmotic flow. By combining this catalytic orientation effect with more powerful, density-dependent acoustic propulsion, both positive and negative rheotaxis can be achieved. The ability to respond to flow stimuli and collectively propel synthetic microswimmers in a directed manner indicates an important step toward practical applications.