Spin-orbit torques, which utilize spin currents arising from the spin-orbit coupling, offer a novel method to electrically switch the magnetization with perpendicular anisotropy. However, the necessity of an external magnetic field to achieve a deterministic switching is an obstacle for realizing practical spin-orbit torque devices with all-electric operation. Here, we report a field-free spin-orbit torque switching by exploiting the domain wall motion in an anti-notched microwire with perpendicular anisotropy, which exhibits multi-domain states stabilized by the domain wall surface tension. The combination of spin-orbit torque, Dzyaloshinskii-Moriya interaction, and domain wall surface tension induced geometrical pinning allows a deterministic control of the domain wall and offers a novel method to achieve a field-free spin-orbit torque switching. Our work demonstrates the proof of concept of a perpendicular memory cell which can be readily adopted in a three-terminal magnetic memory.