Tactile perception is a vital modality of robotic perceptual modalities. However, it is challenging to achieve efficient tactile sensing and minimize power consumption across large areas of robotic artificial skin. While the neuromorphic approach presents a potential solution. This paper proposes a novel bio-inspired tactile perception system for robots based on a neuromorphic scheme. Specifically, a polyvinylidene fluoride (PVDF)-based sensor is initially proposed for acquiring and converting raw tactile signals. Furthermore, we propose a spike-based neuromorphic transformation method for converting raw signals from sensors into spike trains, along with a graph convolutional neural network (GCN) for classifying such data. In order to assess our perceptual system in tactile sensing, particularly in texture recognition, we also created a neuromorphic tactile dataset by rubbing various surfaces with our bionic finger, including sandpaper and fabric surfaces. Subsequently, the network was trained with the dataset. The testing results demonstrated that the texture recognition ability of the bionic finger of this perception system was comparable to that of a human finger.