This research explores using lightweight deep neural network architectures to enable the humanoid robot Pepper to understand American Sign Language (ASL) and facilitate non-verbal human-robot interaction. First, we introduce a lightweight and efficient model for ASL understanding optimized for embedded systems, ensuring rapid sign recognition while conserving computational resources. Building upon this, we employ large language models (LLMs) for intelligent robot interactions. Through intricate prompt engineering, we tailor interactions to allow the Pepper Robot to generate natural Co-Speech Gesture responses, laying the foundation for more organic and intuitive humanoid-robot dialogues. Finally, we present an integrated software pipeline, embodying advancements in a socially aware AI interaction model. Leveraging the Pepper Robot's capabilities, we demonstrate the practicality and effectiveness of our approach in real-world scenarios. The results highlight a profound potential for enhancing human-robot interaction through non-verbal interactions, bridging communication gaps, and making technology more accessible and understandable.