1. In order to authenticate to Jenkins using GitHub, you will have to install the GitHub Authentication Plugin. To do this, click on Manage Jenkins on the panel on the left and on the new page click on Manage Plugins, as shown in the following screenshot:

2. Now you can navigate to the Available tab and type github auth in the search box , as shown in the next screenshot:

3. You can now install the plugin by checking the box on the left and clicking on Install without restart.
4. Once the plugin is installed you can go back to the Jenkins homepage by clicking on the Jenkins logo in the top-left corner and, once again, clicking on Manage Jenkins.
5. This time we will proceed by clicking on Configure Global Security, as shown in the next screenshot:

6. Now head over to GitHub and, as shown in the next screenshot, register a new application by navigating to https://github.com/settings/applications/new:

Here you will need to fill in an arbitrary Application name and the Authorization callback URL as shown. Once you register the application you will be able to see your Client ID and Client Secret. These will be needed in Jenkins in order to fill in the relative fields in the Global Security Settings.

7. Once you submit the form you will be able to log in to Jenkins using your GitHub credentials.