Accurate traffic prediction is a pivotal facet of intelligent transportation systems. While deep learning approaches have shown promise in capturing spatial-temporal dependencies, they heavily rely on extensive historical data and are resource intensive. This paper proposes STEP-LLM, a novel framework that leverages the power of large language models (LLMs) for spatial-temporal traffic prediction. STEP-LLM integrates spatial-temporal-enriched prompting, patch reprogramming of multi-dimensional traffic flow series, and a pre-trained frozen LLM to generate accurate traffic forecasts. The proposed Condensed Spatial Prompting (CSP) method effectively compresses graph interpretations into concise natural language prompts, significantly reducing context length while preserving essential spatial information. Furthermore, a multi-head attention mechanism is employed to align patched time series representations with pre-trained text prototype embeddings, enabling the capture of correlations between multi-dimensional traffic data. Extensive experiments on two real-world datasets demonstrate that STEP-LLM outperforms state-of-the-art specialized traffic prediction models while requiring substantially less computational resources, offering a more efficient and practical solution for real-world traffic prediction applications.