We present the observation of field-free spin-orbit-torque (SOT) switching of magnetization in a ferromagnetic semiconductor (Ga,Mn)As film with four-fold in-plane magnetic anisotropy. Magnetization switching is demonstrated between two orthogonal in-plane easy axes through planar Hall resistance measurements as a current is scanned in the absence of a magnetic field. The chirality of the switching of the current hysteresis loop is consistent with SOT arising from spin polarization caused by Dresselhaus- and Rashba-type spin-orbit-induced effective magnetic fields in the (Ga,Mn)As film. The chirality of magnetization switching can be reversed either by changing the direction of the initial magnetization or by applying a constant external magnetic field bias. The SOT magnetization switching between two states was consistently repeated by applying sequential current pluses with alternating polarities, indicating the potential for developing a field-free SOT device.