Electrical manipulation of magnetization is essential for integration of magnetic functionalities such as magnetic memories and magnetic logic devices into electronic circuits. The current induced spin-orbit torque (SOT) in heavy metal/ferromagnet (HM/FM) bilayers via the spin Hall effect in the HM and/or the Rashba effect at the interfaces provides an efficient way to switch the magnetization. In the meantime, current induced SOT has also been used to switch the in-plane magnetization in single layers such as ferromagnetic semiconductor (Ga,Mn)As and antiferromagnetic metal CuMnAs with globally or locally broken inversion symmetry. Here we demonstrate the current induced perpendicular magnetization switching in L10 FePt single layer. The current induced spin-orbit effective fields in L10 FePt increase with the chemical ordering parameter (S). In 20 nm FePt films with high S, we observe a large charge-to-spin conversion efficiency and a switching current density as low as 7.0E6 A/cm2. We anticipate our findings may stimulate the exploration of the spin-orbit torques in bulk perpendicular magnetic anisotropic materials and the application of high-efficient perpendicular magnetization switching in single FM layer.