Large language models (LLMs), such as ChatGPT, have demonstrated impressive capabilities in various tasks and attracted an increasing interest as a natural language interface across many domains. Recently, large vision-language models (VLMs) like BLIP-2 and GPT-4 have been intensively investigated, which learn rich vision-language correlation from image-text pairs. However, despite these developments, the application of LLMs and VLMs in image quality assessment (IQA), particularly in medical imaging, remains to be explored, which is valuable for objective performance evaluation and potential supplement or even replacement of radiologists' opinions. To this end, this paper introduces IQAGPT, an innovative image quality assessment system integrating an image quality captioning VLM with ChatGPT for generating quality scores and textual reports. First, we build a CT-IQA dataset for training and evaluation, comprising 1,000 CT slices with diverse quality levels professionally annotated. To better leverage the capabilities of LLMs, we convert annotated quality scores into semantically rich text descriptions using a prompt template. Second, we fine-tune the image quality captioning VLM on the CT-IQA dataset to generate quality descriptions. The captioning model fuses the image and text features through cross-modal attention. Third, based on the quality descriptions, users can talk with ChatGPT to rate image quality scores or produce a radiological quality report. Our preliminary results demonstrate the feasibility of assessing image quality with large models. Remarkably, our IQAGPT outperforms GPT-4 and CLIP-IQA, as well as the multi-task classification and regression models that solely rely on images.