Image scrambling technology plays a vital role in the fields of digital watermarking and information hiding. Although traditional image scrambling technology can preprocess images to enhance the security of algorithms, more robust security measures are needed due to the rapid development of artificial intelligence techniques. In order to further improve the security of color image encryption, a color image scrambling technique based on the Chinese remainder theorem and the Arnold transformation is proposed, which combines traditional cryptography with image scrambling techniques. The method initially applies the Arnold transformation to color images, and then encrypts the pixel values of the three channels in the transformed pixel matrix using the Chinese remainder theorem to obtain the final scrambled image. The performance of the algorithm was tested using MATLAB, and the Structural Similarity Index (SSIM) between the original image and the attacked recovered image exceeded 0.9. The correlation between adjacent pixels of the scrambled image approached 0, and the running time was only 46.7s. The algorithm provides a significantly improved and extensive key space compared to using the Chinese remainder theorem or Arnold transform alone. The experimental results show that the algorithm has good resistance to attacks, good scrambling effect and high operational efficiency. The algorithm thoroughly considers both security and operational efficiency aspects, making it suitable for watermark image preprocessing in the field of digital watermarking research, so as to further realize the copyright protection of digital products.