Yes! Generally, you cite anything and everything that comes from somewhere else and isn't common knowledge. Check with your instructor for more information, but all content from the tool you use should be cited.
Content from generative AI like ChatGPT is a nonrecoverable source as it can't be retrieved or linked. It's recommended to base the reference on the style for personal communication, unless your referencing style has specific guidelines.
"Text of prompt" prompt. ChatGPT, Day Month version, OpenAI, Day Month Year, chat.openai.com/chat
Example from MLA: “Describe the symbolism of the green light in the book The Great Gatsby by F. Scott Fitzgerald” prompt. ChatGPT, 13 Feb. version, OpenAI, 8 Mar. 2023, chat.openai.com/chat.
In text example from MLA: ("Describe the symbolism")
OpenAI. (2023). ChatGPT (Month Day version) [Large language model]. https://chat.openai.com/chat
Example from APA: OpenAI. (2023). ChatGPT (Mar 14 version) [Large language model]. https://chat.openai.com/chat
APA recommends describing how you used the tool in your Method section or a comparable section of your paper. If your paper doesn't have a comparable section, you might describe how you used the tool in your introduction. In the text of your paper, provide the prompt you used and then any portion of the relevant text that was generated in response.
This fabulous guide from RMIT University Library explains how to cite AI generated images in various citation styles.