Claude Code comes with every paid Claude plan, and Codex comes with ChatGPT plans. Both can change your theme and run WordPress commands once they can reach your site.
There are two common ways to give them that reach. The first is a copy of your site’s code on your computer: you keep track of changes, test them and upload them yourself. WordPress.com’s Studio tools support this and name Claude Code among the AI tools they work with.
The second is working on the server itself. Claude Code’s desktop app can connect to a server and installs itself there the first time; the server needs enough space and the right setup. Codex can work on a server after you install it and sign in there. Either way, someone has to set up access to the server first.
Both tools let you choose how much the AI may do without asking. Claude Code can undo its own file edits, but not changes made by commands, so database changes need their own backups.