Large language models (LLMs) have demonstrated potential in fact-checking claims, yet their capabilities in verifying claims in multilingual contexts remain largely understudied. This paper investigates the efficacy of various prompting techniques, viz. Zero-Shot, English Chain-of-Thought, Self-Consistency, and Cross-Lingual Prompting, in enhancing the fact-checking and claim-verification abilities of LLMs for Arabic claims. We utilize 771 Arabic claims sourced from the X-fact dataset to benchmark the performance of four LLMs. To the best of our knowledge, ours is the first study to benchmark the inherent Arabic fact-checking abilities of LLMs stemming from their knowledge of Arabic facts, using a variety of prompting methods. Our results reveal significant variations in accuracy across different prompting methods. Our findings suggest that Cross-Lingual Prompting outperforms other methods, leading to notable performance gains.