In github, you can create a 'deploy key' for a repository.
This key will only be valid for that repository.
First, create a key pair.
In github, navigate to your repository's homepage and click on Settings.
Click on 'Deploy keys' and then click 'Add deploy key'.
Give it a name and paste the public key and save it.
In AWX, create a 'Source Control' credential type.
Give it a name and paste the private key into the box (and also the passphrase if you used one) and save it.
In your project definition, set the Source Code Credential to the credential you just created and save it.