In the Fundamentals of Laparoscopic Surgery (FLS) standard medical training regimen, the Pattern Cutting task requires residents to demonstrate proficiency by maneuvering two tools, surgical scissors and tissue gripper, to accurately cut a circular pattern on surgical gauze suspended at the corners. Accuracy of cutting depends on tensioning, wherein the gripper pinches a point on the gauze in R3 and pulls to induce and maintain tension in the material as cutting proceeds. An automated tensioning policy maps the current state of the gauze to output a direction of pulling as an action. The optimal tensioning policy depends on both the choice of pinch point and cutting trajectory. We explore the problem of learning a tensioning policy conditioned on specific cutting trajectories. Every timestep, we allow the gripper to react to the deformation of the gauze and progress of the cutting trajectory with a translation unit vector along an allowable set of directions. As deformation is difficult to analytically model and explicitly observe, we leverage deep reinforcement learning with direct policy search methods to learn tensioning policies using a finite-element simulator and then transfer them to a physical system. We compare the Deep RL tensioning policies with fixed and analytic (opposing the error vector with a fixed pinch point) policies on a set of 17 open and closed curved contours in simulation and 4 patterns in physical experiments with the da Vinci Research Kit (dVRK). Our simulation results suggest that learning to tension with Deep RL can significantly improve performance and robustness to noise and external forces.