Sign words are the building blocks of any sign language. In this work, we present wSignGen, a word-conditioned 3D American Sign Language (ASL) generation model dedicated to synthesizing realistic and grammatically accurate motion sequences for sign words. Our approach leverages a transformer-based diffusion model, trained on a curated dataset of 3D motion meshes from word-level ASL videos. By integrating CLIP, wSignGen offers two advantages: image-based generation, which is particularly useful for children learning sign language but not yet able to read, and the ability to generalize to unseen synonyms. Experiments demonstrate that wSignGen significantly outperforms the baseline model in the task of sign word generation. Moreover, human evaluation experiments show that wSignGen can generate high-quality, grammatically correct ASL signs effectively conveyed through 3D avatars.