Sign language serves as an integral communication medium for the hard-of-hearing and deaf community. However, the lack of efficient recognition systems often leads to barriers in interaction between signers and non-signers. This study presents a real-time Sign Language Recognition System (SLR) system implemented on the Jetson Nano, leveraging its GPU-accelerated deep learning capabilities for high-speed and accurate recognition. The system uses transfer learning approach with the pre-trained InceptionV3 architecture as the base model to recognize American Sign Language (ASL) fingerspelling and progressively form sentences. To further enhance the model performance, we created a custom dataset of 12,025 images spread across 25 classes, i.e., 24 ASL letters and one blank class. By optimizing deep learning inference on the Jetson Nano, this work ensures real-time processing on edge devices, advancing accessibility and promoting social inclusivity for the deaf community.