Spin-orbit qubit (SOQ) is the dressed spin by the orbital degree of freedom through a strong spin-orbit coupling. We show that Coulomb interaction between two electrons in quantum dots located separately in two nanowires can efficiently induce quantum entanglement between two SOQs. The physical mechanism to achieve such quantum entanglement is based on the feasibility of the SOQ responding to the external electric field via an intrinsic electric dipole spin resonance.