You can use workflow triggers
Triggers are a powerful tool for keeping your JIRA issues synchronized with the information in your development tools (FishEye/Crucible, Bitbucket and GitHub).
But your development tool has to be in the following list :
- Bitbucket Server (all current versions)
- FishEye/Crucible (all current versions)
- GitHub Enterprise 11.10.290 (or later)
- Bitbucket
- GitHub
One other solution would be to install the Git Integration Plugin for JIRA but it's not free. (You can maybe try to apply to Community, Open Source or Classroom License)
According to their documentation :
Git Integration Plugin for JIRA supports most or all git servers including:
GitLab, Microsoft Team Foundation Server, Team Services, GitHub, BitBucket, BitBucket Server, Beanstalk, Git on Linux, Bonobo, Git on Windows, Gitolite, Gerrit, GitBlit, Windows share, SSH, HTTP, HTTPS, git protocol, local file path, and network path.