It is not possible to transform an issue into a PR from Github UI. However, it's possible from the API.
Deploy this application, register the webhook and then, pushing branches following the issue-XXX pattern will lead to the XXX issue being turned into a PR with the code of the branch.
https://turn-issue-into-pr.herokuapp.com/webhook/issue-to-pr can be registered as a webhook. This webhook listens to the create event. Currently, it only works on repos where i (@DavidBruant) have write access, but it's easy to deploy it yourself.
MIT