Drifting is a complicated task for autonomous vehicle control. Most traditional methods in this area are based on motion equations derived by the understanding of vehicle dynamics, which is difficult to be modeled precisely. We propose a robust drift controller without explicit motion equations, which is based on the latest model-free deep reinforcement learning algorithm soft actor-critic. The drift control problem is formulated as a trajectory following task, where the error-based state and reward are designed. After being trained on tracks with different levels of difficulty, our controller is capable of making the vehicle drift through various sharp corners quickly and stably in the unseen map. The proposed controller is further shown to have excellent generalization ability, which can directly handle unseen vehicle types with different physical properties, such as mass, tire friction, etc.