The process of acoustically stimulated charge transport in the graphene film on the surface of the YZ-cut of a LiNbO3 crystal was investigated. It was found that the dependence of the current in the graphene film on the frequency of the surface acoustic wave (SAW) excitation repeats the amplitude-frequency response of the SAW delay time line. It is shown that increasing the SAW amplitude leads to an increase in the current in the graphene film, and the current in the graphene film depends linearly on the amplitude of the high-frequency input signal supplied to the interdigital transducer (IDT, in dB). It is demonstrated that at a positive bias potential on the graphene film, the SAW propagation allows to change the direction of the current in the graphene film by changing the amplitude of the SAW. It is also shown that in the frequency range of the amplitude-frequency response of the SAW delay time line, the current in the graphene film can vary from positive to negative values depending on the frequency. The capability to control the SAW excitation frequency or the SAW amplitude makes it possible to control the value and direction of the current in the graphene film. The SAW propagation lets to collect and transport the photo-stimulated charges in the graphene film on the crystal surface.