Forensics research has developed several techniques to identify the model and manufacturer of a digital image or videos source camera. However, to the best of our knowledge, no work has been performed to identify the manufacturer and model of the scanner that captured an MRI image. MRI source identification can have several important applications ranging from scientific fraud discovery, exposing issues around anonymity and privacy of medical records, protecting against malicious tampering of medical images, and validating AI-based diagnostic techniques whose performance varies on different MRI scanners. In this paper, we propose a new CNN-based approach to learn forensic traces left by an MRI scanner and use these traces to identify the manufacturer and model of the scanner that captured an MRI image. Additionally, we identify an issue called weight divergence that can occur when training CNNs using a constrained convolutional layer and propose three new correction functions to protect against this. Our experimental results show we can identify an MRI scanners manufacturer with 97.88% accuracy and its model with 91.07% accuracy. Additionally, we show that our proposed correction functions can noticeably improve our CNNs accuracy when performing scanner model identification.