Traffic prediction is a vital component of intelligent transportation systems. By reasoning about traffic patterns in both the spatial and temporal dimensions, accurate and interpretable predictions can be provided. A considerable challenge in traffic prediction lies in handling the diverse data distributions caused by vastly different traffic conditions occurring at different locations. LLMs have been a dominant solution due to their remarkable capacity to adapt to new datasets with very few labeled data samples, i.e., few-shot adaptability. However, existing forecasting techniques mainly focus on extracting local graph information and forming a text-like prompt, leaving LLM- based traffic prediction an open problem. This work presents a probabilistic LLM for traffic forecasting with three highlights. We propose a graph-aware LLM for traffic prediction that considers proximal traffic information. Specifically, by considering the traffic of neighboring nodes as covariates, our model outperforms the corresponding time-series LLM. Furthermore, we adopt a lightweight approach for efficient domain adaptation when facing new data distributions in few-shot fashion. The comparative experiment demonstrates the proposed method outperforms the state-of-the-art LLM-based methods and the traditional GNN- based supervised approaches. Furthermore, Strada-LLM can be easily adapted to different LLM backbones without a noticeable performance drop.