This is currently not possible, see Allow wiki edits from non-members in project wikis (#25177) · Issue · gitlab-org/gitlab. This ticket was opened in November 2018. It was closed in September 2025 by Matthew Macfarlane. The reason given was: "we have decided that this request will not be prioritized in our upcoming 12-24 month plans, and as such, will close this issue in an effort to reduce the noise in our product backlog." (copied 2025-12-04)

Contributor Markus Koller explained in October 2020 the current status:

Currently, write permission in wikis is hard-coded to members with role "Developer" and above.