In this work, we study the rotating magnetic field driven domain wall (DW) motion in antiferromagnetic nanowires, using the micromagnetic simulations of the classical Heisenberg spin model. We show that in low frequency region, the rotating field alone could efficiently drive the DW motion even in the absence of Dzyaloshinskii-Moriya interaction (DMI). In this case, the DW rotates synchronously with the magnetic field, and a stable precession torque is available and drives the DW motion with a steady velocity. In large frequency region, the DW only oscillates around its equilibrium position and cannot propagate. The dependences of the velocity and critical frequency differentiating the two motion modes on several parameters are investigated in details, and the direction of the DW motion can be controlled by modulating the initial phase of the field. Interestingly, a unidirectional DW motion is predicted attributing to the bulk DMI, and the nonzero velocity for high frequency is well explained. Thus, this work does provide useful information for further antiferromagnetic spintronics applications.