This study explores the capability of Large Language Models (LLMs) to evaluate causality in causal graphs generated by conventional statistical causal discovery methods-a task traditionally reliant on manual assessment by human subject matter experts. To bridge this gap in causality assessment, LLMs are employed to evaluate the causal relationships by determining whether a causal connection between variable pairs can be inferred from textual context. Our study compares two approaches: (1) prompting-based method for zero-shot and few-shot causal inference and, (2) fine-tuning language models for the causal relation prediction task. While prompt-based LLMs have demonstrated versatility across various NLP tasks, our experiments on biomedical and general-domain datasets show that fine-tuned models consistently outperform them, achieving up to a 20.5-point improvement in F1 score-even when using smaller-parameter language models. These findings provide valuable insights into the strengths and limitations of both approaches for causal graph evaluation.