The physical implementation of quantum gates with high fidelity is one of the key technologies of quantum computation and quantum communication. Based on the circuit quantum electrodynamics and circuit quantum acoustodynamics theory, a quantum gate scheme composed of two superconducting transmon qubits with long coherence time and a film bulk acoustic wave resonator (FBAR) with high mechanical quality factor is proposed in this paper. The bulk acoustic resonator acts as a microwave photon channel, which enables quantum state exchange between two transmon qubits. In this paper, the equivalent circuit of bulk acoustic resonator is analyzed by the Butterworth Van Dyke model, and the quantized Hamiltonian of the system is constructed, then the quantum state of the system is encoded in the form of two level atom phonon mixed quantum state. The input state of the system is controlled by adjusting the external magnetic field, and the output state of the system can be obtained by the measurement module. Under the Jaynes Cummings model, the system can complete quantum iSWAP gate operation with high fidelity.