The optical geometric phase encoded by the in-plane spatial orientation of microstructures has promoted the rapid development of numerous new-type optical meta-devices. However, pushing the concept of the geometric phase toward the acoustic community still faces challenges. In this work, we take advantage of two acoustic nonlocal metagratings that could support the direct conversion between plane wave and designated vortex mode, of which the orbital angular momentum conversion process plays a vital role in obtaining the acoustic geometric phase. We obtain the acoustic geometric phases of different orders by merely varying the orientation angle of one of the acoustic nonlocal metagratings. Intriguingly, according to our developed theory, we reveal that the reflective acoustic geometric phase, which is twice of the transmissive one, can be readily realized by transferring the transmitted configuration to a reflected one. Both the theoretical model and experimental measurements successfully verify the announced transmissive and reflective acoustic geometric phases. Moreover, the characteristics of reconfigurability and continuous phase modulation that covers the 2{\pi} range shown by the acoustic geometric phases provide us with new possibilities in advanced acoustic wavefront control.