Perching on structures such as trees, beams, and ledges is essential for extending the endurance of aerial robots by enabling energy conservation in standby or observation modes. A tethered tensile perching mechanism offers a simple, adaptable solution that can be retrofitted to existing robots and accommodates a variety of structure sizes and shapes. However, tethered tensile perching introduces significant modelling challenges which require precise management of aerial robot dynamics, including the cases of tether slack & tension, and momentum transfer. Achieving smooth wrapping and secure anchoring by targeting a specific tether segment adds further complexity. In this work, we present a novel trajectory framework for tethered tensile perching, utilizing reinforcement learning (RL) through the Soft Actor-Critic from Demonstrations (SACfD) algorithm. By incorporating both optimal and suboptimal demonstrations, our approach enhances training efficiency and responsiveness, achieving precise control over position and velocity. This framework enables the aerial robot to accurately target specific tether segments, facilitating reliable wrapping and secure anchoring. We validate our framework through extensive simulation and real-world experiments, and demonstrate effectiveness in achieving agile and reliable trajectory generation for tensile perching.