This isn't currently possible, but one solution is to configure issue creation from email, as this will allow guest users to create issues by mailing their problem to a mialbox that JIRA periodically scans and creates a JIRA issue out of each of the emails in the mailbox. You can read about configuring issue creation from email here: https://confluence.atlassian.com/display/AOD/Creating+Issues+and+Comments+from+Email
All the best,
Unless I'm mistaken this may be what you're looking for:
This allows your web site visitors to give you feedback and have that feedback appear as an issue in a specific JIRA project. I attached ours to a project specifically for this feedback and then any feature requests that get adopted are moved to the appropriate project and enter that project's workflow.
The Issue Collector has the same problem as creating issues with mail: the issue is created with the sender, but only when the sender is a recognized Jira user and/or when you configure it in such a way that the user is automatically created (which goes towards your license).
In other words: guest-users are not possible.
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