Spin–orbit torque (SOT) induced magnetization switching in an energy-efficient and fast way has exhibited great application potential in next generation magnetic memories. However, a complicated layer structure is usually needed to break the mirror symmetry for achieving SOT induced field-free magnetization switching. Here, we report a sizeable field-free magnetization switching through large out-of-plane SOT in the chemically disordered A1-CoxPt100−x single layers within a Co composition range from 40 to 70. The largest absolute out-of-plane SOT efficiency is found at its equiatomic concentration (Co50Pt50), in which the absolute in-plane SOT efficiency also reaches the maximum value, 22.7 Oe/107 A cm−2. We further demonstrate that the symmetry dependence of field-free magnetization switching might arise from the chemically ordered L11-CoPt nano-scaled platelets formed during the sample deposition. We expect that the experimental identification of the field-free magnetization switching in the ferromagnetic CoPt single layer is desirable to simplify the applications of spin logic devices.