Sign Language Recognition (SLR) plays a crucial role in bridging the communication gap between the hearing-impaired community and society. This paper introduces SLRNet, a real-time webcam-based ASL recognition system using MediaPipe Holistic and Long Short-Term Memory (LSTM) networks. The model processes video streams to recognize both ASL alphabet letters and functional words. With a validation accuracy of 86.7%, SLRNet demonstrates the feasibility of inclusive, hardware-independent gesture recognition.