The advances in the Neural Radiance Fields (NeRF) research offer extensive applications in diverse domains, but protecting their copyrights has not yet been researched in depth. Recently, NeRF watermarking has been considered one of the pivotal solutions for safely deploying NeRF-based 3D representations. However, existing methods are designed to apply only to implicit or explicit NeRF representations. In this work, we introduce an innovative watermarking method that can be employed in both representations of NeRF. This is achieved by fine-tuning NeRF to embed binary messages in the rendering process. In detail, we propose utilizing the discrete wavelet transform in the NeRF space for watermarking. Furthermore, we adopt a deferred back-propagation technique and introduce a combination with the patch-wise loss to improve rendering quality and bit accuracy with minimum trade-offs. We evaluate our method in three different aspects: capacity, invisibility, and robustness of the embedded watermarks in the 2D-rendered images. Our method achieves state-of-the-art performance with faster training speed over the compared state-of-the-art methods. Project page: https://kuai-lab.github.io/cvpr2024waterf/