Robots are increasingly envisioned as human companions, assisting with everyday tasks that often involve manipulating deformable objects. Despite recent advances in robotic hardware and embodied AI, existing systems continue to struggle with handling thin, flat, and deformable objects such as paper and fabric. These limitations stem from the lack of robust perception techniques for reliable state estimation under diverse visual conditions and the absence of planning methods capable of generating effective grasping motions. To address these limitations, we propose PP-Tac, a robotic system designed to pick up paper-like objects. PP-Tac incorporates a multi-fingered robotic hand equipped with high-resolution, hemispherical tactile sensors (R-Tac) that provide omnidirectional tactile feedback. This hardware configuration enables real-time slip detection and online force control to mitigate slippage during manipulation. Grasp motion generation is accomplished through a trajectory synthesis pipeline, which constructs a dataset of pinching motions and trains a diffusion-based policy to control the hand-finger simultaneously. Experiment results show that PP-Tac successfully grasps paper-like objects with varying material, thickness, and stiffness, achieving an overall success rate of 87.5%. To the best of our knowledge, this is the first system to successfully grasp paper-like deformable objects using a tactile dexterous hand.