Neural Radiance Fields (NeRF) have been gaining attention as a significant form of 3D content representation. With the proliferation of NeRF-based creations, the need for copyright protection has emerged as a critical issue. Although some approaches have been proposed to embed digital watermarks into NeRF, they often neglect essential model-level considerations and incur substantial time overheads, resulting in reduced imperceptibility and robustness, along with user inconvenience. In this paper, we extend the previous criteria for image watermarking to the model level and propose NeRF Signature, a novel watermarking method for NeRF. We employ a Codebook-aided Signature Embedding (CSE) that does not alter the model structure, thereby maintaining imperceptibility and enhancing robustness at the model level. Furthermore, after optimization, any desired signatures can be embedded through the CSE, and no fine-tuning is required when NeRF owners want to use new binary signatures. Then, we introduce a joint pose-patch encryption watermarking strategy to hide signatures into patches rendered from a specific viewpoint for higher robustness. In addition, we explore a Complexity-Aware Key Selection (CAKS) scheme to embed signatures in high visual complexity patches to enhance imperceptibility. The experimental results demonstrate that our method outperforms other baseline methods in terms of imperceptibility and robustness.