Recently, large language models (LLMs) with hundreds of billions of parameters have demonstrated the emergent ability, surpassing traditional methods in various domains even without fine-tuning over domain-specific data. However, when it comes to financial sentiment analysis (FSA)$\unicode{x2013}$a fundamental task in financial AI$\unicode{x2013}$these models often encounter various challenges, such as complex financial terminology, subjective human emotions, and ambiguous inclination expressions. In this paper, we aim to answer the fundamental question: whether LLMs are good in-context learners for FSA? Unveiling this question can yield informative insights on whether LLMs can learn to address the challenges by generalizing in-context demonstrations of financial document-sentiment pairs to the sentiment analysis of new documents, given that finetuning these models on finance-specific data is difficult, if not impossible at all. To the best of our knowledge, this is the first paper exploring in-context learning for FSA that covers most modern LLMs (recently released DeepSeek V3 included) and multiple in-context sample selection methods. Comprehensive experiments validate the in-context learning capability of LLMs for FSA.