We developed an American Sign Language (ASL) learning platform in a Virtual Reality (VR) environment to facilitate immersive interaction and real-time feedback for ASL learners. We describe the first game to use an interactive teaching style in which users learn from a fluent signing avatar and the first implementation of ASL sign recognition using deep learning within the VR environment. Advanced motion-capture technology powers an expressive ASL teaching avatar within an immersive three-dimensional environment. The teacher demonstrates an ASL sign for an object, prompting the user to copy the sign. Upon the user's signing, a third-party plugin executes the sign recognition process alongside a deep learning model. Depending on the accuracy of a user's sign production, the avatar repeats the sign or introduces a new one. We gathered a 3D VR ASL dataset from fifteen diverse participants to power the sign recognition model. The proposed deep learning model's training, validation, and test accuracy are 90.12%, 89.37%, and 86.66%, respectively. The functional prototype can teach sign language vocabulary and be successfully adapted as an interactive ASL learning platform in VR.