Early screening of chronic kidney disease (CKD) is critical for timely intervention, yet most machine learning (ML) and deep learning (DL) approaches require labeled data and model training, limiting their use in real-world screening settings. This study evaluates the effectiveness of large language models (LLMs) for CKD screening under zero-shot and few-shot in-context learning settings and compares them with traditional ML and DL methods. We propose a framework that uses clinically selected tabular features and structured prompt templates to enable LLM-based inference without task-specific training. LLM performance is evaluated across multiple prompt styles, feature configurations, and data settings, and compared with standard ML, DL, and tabular foundation model (TFM) baselines, and existing CKD screening tools. The results show that LLMs can achieve competitive performance using only a small number of examples, often matching or outperforming traditional approaches in low-data settings. However, their performance remains model-dependent and less stable as input complexity increases. In contrast, ML, DL, and TFM models show more consistent improvement with larger training data. Overall, the findings highlight a trade-off between data efficiency and stability, suggesting that LLMs may serve as a flexible complementary approach for CKD screening when labeled data are limited. To facilitate further research and reproducibility, the code has been made publicly available at https://github.com/akabircs/LLM4CKD

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