Only repository collaborators can edit a public repository's wiki by default, but you can allow anyone with an account on GitHub.com to edit your wiki.
Who can use this feature?
Wikis are available in public repositories with GitHub Free and GitHub Free for organizations, and in public and private repositories with GitHub Pro, GitHub Team, GitHub Enterprise Cloud and GitHub Enterprise Server. For more information, see "GitHub’s plans."
On GitHub.com, navigate to the main page of the repository.
Under your repository name, click Settings. If you cannot see the "Settings" tab, select the dropdown menu, then click Settings.
Under Features, unselect Restrict editing to collaborators only.