Code translation is an essential task in software migration, multilingual development, and system refactoring. Recent advancements in large language models (LLMs) have demonstrated significant potential in this task. However, prior studies have highlighted that LLMs often struggle with domain-specific code, particularly in resolving cross-lingual API mappings. To tackle this challenge, we propose APIRAT, a novel code translation method that integrates multi-source API knowledge. APIRAT employs three API knowledge augmentation techniques, including API sequence retrieval, API sequence back-translation, and API mapping, to guide LLMs to translating code, ensuring both the correct structure of API sequences and the accurate usage of individual APIs. Extensive experiments on two public datasets, CodeNet and AVATAR, indicate that APIRAT significantly surpasses existing LLM-based methods, achieving improvements in computational accuracy ranging from 4% to 15.1%. Additionally, our evaluation across different LLMs showcases the generalizability of APIRAT. An ablation study further confirms the individual contributions of each API knowledge component, underscoring the effectiveness of our approach.