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Abstract Magnetization in a ferromagnetic layer could be manipulated by the spin-orbit torque whose generation commonly relies on the spin-orbit coupling from the adjacent heavy-metal layer within the bilayer. The fact that the magnetic topological insulator possesses both the ferromagnetic order with perpendicular anisotropy and inherent spin-orbit coupling inspires to realize such a torque-induced magnetization switching without forming any heterostructure with other materials. Here, only using a single layer of magnetically-doped topological insulator Cr:(Bi,Sb)2Te3, we realize a magnetization switching only by applying a large dc current. Assisted by the magnetic history, such a switching behaves nonvolatile under zero field but becomes volatile otherwise, as consistently shown by magnetoelectric transports and magneto-optical Kerr effect measurements. Static and quasistatic current are found to be equivalent for the switching. We propose that this switching may associate with the torque resulted from the spin-orbit coupling and the compositional asymmetry in the Cr-profile of the single layer.