Fallacies are defective arguments with faulty reasoning. Detecting and classifying them is a crucial NLP task to prevent misinformation, manipulative claims, and biased decisions. However, existing fallacy classifiers are limited by the requirement for sufficient labeled data for training, which hinders their out-of-distribution (OOD) generalization abilities. In this paper, we focus on leveraging Large Language Models (LLMs) for zero-shot fallacy classification. To elicit fallacy-related knowledge and reasoning abilities of LLMs, we propose diverse single-round and multi-round prompting schemes, applying different taskspecific instructions such as extraction, summarization, and Chain-of-Thought reasoning. With comprehensive experiments on benchmark datasets, we suggest that LLMs could be potential zero-shot fallacy classifiers. In general, LLMs under single-round prompting schemes have achieved acceptable zeroshot performances compared to the best fullshot baselines and can outperform them in all OOD inference scenarios and some opendomain tasks. Our novel multi-round prompting schemes can effectively bring about more improvements, especially for small LLMs. Our analysis further underlines the future research on zero-shot fallacy classification. Codes and data are available at: https://github.com/panFJCharlotte98/Fallacy_Detection.