We report on the novel valley acoustoelectric effect, which can arise in a 2D material, like a transition metal dichalcogenide monolayer, residing on a piezoelectric substrate. The essence of this effect lies in the emergence of a drag electric current (and a spin current) due to a propagating surface acoustic wave. This current consists of three contributions, one independent of the valley index and proportional to the acoustic wave vector, the other arising due to the trigonal warping of the electron dispersion, and the third one is due to the Berry phase, which Bloch electrons acquire traveling along the crystal. As a result, there appear components of the current orthogonal to the acoustic wave vector. Further, we build an angular pattern, encompassing nontrivial topological properties of the acoustoelectric current, and suggest a way to run and measure the conventional diffusive, warping, and acoustoelectric valley Hall currents independently. We develop a theory, which opens a way to manipulate valley transport by acoustic methods, expanding the applicability of valleytronic effects on acoustoelectronic devices.