Medical image copyright protection is becoming increasingly relevant as medical images are used more frequently in medical networks and institutions. The traditional embedded watermarking system is inappropriate for medical images since it degrades the original images’ quality. Furthermore, medical-colored image watermarking options are constrained since most medical watermarking systems are built for gray-scale images. This paper proposes a zero-watermarking scheme for medical color image copyright protection based on a chaotic system and Resnet50, which is a convolutional neural network method. The network Resnet50 is used to extract features from the color medical image, and then a logistic Gaussian map is used to scramble these features and scramble the binary image. Finally, an exclusive OR operation is performed (scrambled binary image, scrambled features for the medical color image) to form a zero watermarking. The experimental result proves that our scheme is effective and robust to geometric and common image processing attacks. The BER values of the extracted watermarks are below 0.0039, and the NCC values are above 0.9942, while the average PSNR values of the attacked images are 29.0056 dB. Also, it is superior to other zero-watermark schemes for medical images in terms of robustness to conventional image processing and geometric attacks. Furthermore, the experimental results show that the Resnet50 model outperforms other models in terms of reducing the mean squared errors of the features between the attacked and original image.