We propose a direct axion dark matter (DM) search using superconducting transmon qubits as quantum sensors. With an external magnetic field applied, axion DM generates an oscillatingelectric field which causes the excitation of the qubit; such an excitation can be regarded as a signal of the axion DM. We provide a theoretical consideration of the excitation process of the qubits taking into account the effects of the shielding cavity surrounding the qubits and estimate the signal rate for the axion DM detection. We also discuss the enhancement of the DM signal by using cavity resonance and entangled quantum sensors realized by a quantum circuit. Combining these two effects, we can reach the parameter region suggested by QCD axion models.