Reliable polymer identification is essential for ensuring the quality and safety of recycled plastics, yet conventional sorting and spectroscopic techniques often struggle to deliver robust discrimination. Terahertz (THz) spectroscopy offers a promising alternative, providing high-resolution and non-destructive measurements. In this work, we leverage THz signals to classify 12 types of polymers, including pure polymers, multilayer films, commercial blends, and biopolymers. To handle the complexity of these spectral signals, we propose the Multi-Scale Feature Attention Network (MSFAN), a novel deep learning architecture tailored for THz data. The framework integrates feature gating for signal recalibration and multi-scale parallel convolutions to capture diverse frequency patterns. These features are further refined through cross-feature attention and attention pooling, enabling the model to intrinsically highlight the most informative THz regions. MSFAN consistently outperforms state-of-the-art models, reaching a classification accuracy of 85.2%. This study demonstrates the potential of combining THz spectroscopy with deep learning techniques for effective, scalable, and interpretable polymer classification.