Robots are increasingly envisioned as human companions, assisting with everyday tasks that often involve manipulating deformable objects. Although recent advances in robotic hardware and embodied AI have expanded their capabilities, current systems still struggle with handling thin, flat, and deformable objects such as paper and fabric. This limitation arises from the lack of suitable perception techniques for robust state estimation under diverse object appearances, as well as the absence of planning techniques for generating appropriate grasp motions. To bridge these gaps, this paper introduces PP-Tac, a robotic system for picking up paper-like objects. PP-Tac features a multi-fingered robotic hand with high-resolution omnidirectional tactile sensors \sensorname. This hardware configuration enables real-time slip detection and online frictional force control that mitigates such slips. Furthermore, grasp motion generation is achieved through a trajectory synthesis pipeline, which first constructs a dataset of finger's pinching motions. Based on this dataset, a diffusion-based policy is trained to control the hand-arm robotic system. Experiments demonstrate that PP-Tac can effectively grasp paper-like objects of varying material, thickness, and stiffness, achieving an overall success rate of 87.5\%. To our knowledge, this work is the first attempt to grasp paper-like deformable objects using a tactile dexterous hand. Our project webpage can be found at: https://peilin-666.github.io/projects/PP-Tac/