Image generative models have become increasingly popular, but training them requires large datasets that are costly to collect and curate. To circumvent these costs, some parties may exploit existing models by using the generated images as training data for their own models. In general, watermarking is a valuable tool for detecting unauthorized use of generated images. However, when these images are used to train a new model, watermarking can only enable detection if the watermark persists through training and remains identifiable in the outputs of the newly trained model - a property known as radioactivity. In this work, we are the first to propose a radioactive watermarking method tailored for IARs - drawing inspiration from techniques in large language models (LLMs), which share IARs' autoregressive paradigm. Our extensive experimental evaluation highlights our method's effectiveness in preserving radioactivity within IARs, enabling robust provenance tracking, and preventing unauthorized use of their generated images.