The acoustoelectric effect in graphene is studied in a graphene/lithium niobate hybrid system, which was prepared by transferring large area single-layer graphene grown on copper onto lithium niobate SAW devices. The transfer of momentum from the surface acoustic waves (SAWs), generated on the surface of the lithium niobate, to the carriers in graphene results in an attenuation and velocity shift of the wave, and gives rise to an acoustoelectric current. The acoustoelectric current, and the amplitude and velocity of the SAW are measured using a sourcemeter and oscilloscope, respectively. Macroscopic acoustoelectric current flowing over several hundred micrometers is demonstrated in graphene, which is measured to be directly proportional to the SAW intensity and frequency at room temperature. A relatively simple classical relaxation model, which describes the piezoelectric interaction between SAWs and the carriers in a two-dimensional electron system, is used to explain the experimental observations. The investigation of the acoustoelectric current as a function of temperature demonstrates the ability of SAWs of different wavelengths to probe graphene at different length scales. By tuning the conductivity of the graphene through the use of a top gate, voltage-controlled phase (velocity) shifters are demonstrated. The acoustoelectric current measured as a function of gate voltage demonstrates that an equal density of electrons and holes are transported at the charge neutrality point, reflecting the unique properties of graphene.