Recent advancements in synthesis and sequencing techniques have made deoxyribonucleic acid (DNA) a promising alternative for next-generation digital storage. As it approaches practical application, ensuring the security of DNA-stored information has become a critical problem. Deniable encryption allows the decryption of different information from the same ciphertext, ensuring that the "plausible" fake information can be provided when users are coerced to reveal the real information. In this paper, we propose a deniable encryption method that uniquely leverages DNA noise channels. Specifically, true and fake messages are encrypted by two similar modulation carriers and subsequently obfuscated by inherent errors. Experiment results demonstrate that our method not only can conceal true information among fake ones indistinguishably, but also allow both the coercive adversary and the legitimate receiver to decrypt the intended information accurately. Further security analysis validates the resistance of our method against various typical attacks. Compared with conventional DNA cryptography methods based on complex biological operations, our method offers superior practicality and reliability, positioning it as an ideal solution for data encryption in future large-scale DNA storage applications.