As a typical deformable linear object (DLO), flexible wires have very wide applications, and in recent years, there has been increasing focus on robotic manipulation of wires. Traditional rigid control methods often struggle to cope with the nonlinear deformation and uncertainties of wires during manipulation. Most previous studies have employed a combination of vision and tactile sensing to accomplish tasks such as grasping, socket insertion, or planar wiring, and there are also efforts focused on shape control of wires. This paper focuses on using only a single tactile perception to complete the robot’s compliant following of wires and the fixed-trajectory wiring operation in three-dimensional space. To this end, we propose a robot control framework based on tactile sensing for the automated manipulation of flexible wires. Firstly, the recognition of the wire posture inside the tactile gripper was completed. Next, we introduce a tactile servo control method based on Deep Deterministic Policy Gradient (DDPG). Finally, we define the overall algorithm framework to carry out the specific task. The experimental results show that our design is competent for this task. It expands the limitations of planar wiring and is capable of completing the wire routing task while performing specific three-dimensional space trajectories.