Under the Digital Image and Communication in Medicine (DICOM) standard, the Advanced Encryption Standard (AES) is used to encrypt medical image pixel data. This highly sensitive data needs to be transmitted securely over networks to prevent data modification. Therefore, there is ongoing research into how well encryption algorithms perform on medical images and whether they can be improved. In this paper, we have developed an algorithm using a chaotic map combined with AES and tested it against AES in its standard form. This comparison allowed us to analyse how the chaotic map affected the encryption quality. The developed algorithm, CAT-AES, iterates through Arnold’s cat map before encryption a certain number of times whereas, the standard AES encryption does not. Both algorithms were tested on two sets of 16-bit DICOM images: 20 brain MRI and 26 breast cancer MRI scans, using correlation coefficient and histogram uniformity for evaluation. The results showed improvements in the encryption quality. When encrypting the images with CAT-AES, the histograms were more uniform, and the absolute correlation coefficient was closer to zero for the majority of images tested on.