In the current 7th edition of the American Psychological Association (APA7) style guide, citations of generative AI are not addressed. There are mainly two pragmatic solutions to the problem circulating among APA7 users.
On the one hand, it is proposed to cite ChatGPT (and other generative AI tools) in the same way as other non-recoverable sources such as personal communication. In this case, the AI tool is only cited in the text as interlocutor with a given date of the communication, but not included in the bibliography/list of works cited. (See APA Style Blog.)
Example
In the text: … (OpenAI, personal communication, April 18, 2023)
In the bibliography: no entry
The approach currently favored by the APA is to treat the outputs generated by AI tools as the results of algorithms or programs. This involves citing the author’s name and year in the text and creating an entry in the bibliography. (See APA Style Blog.)
Example
In the text: … (OpenAI, 2023)
In the bibliography: OpenAI. (2023). ChatGPT (Mar 14 version) [Large language model]. https://chat.openai.com/chat
If required, the complete output of the AI can be listed in the appendix.
Example
In the text: … (OpenAI, 2023; see Appendix A for the full transcript)
Other Guidelines for Scientific Writing
The authors and users of other guidelines for academic writing, such as Chicago Style or Harvard, suggest similar approaches. (See the German and English summaries on scribbr)