I am aware that there are many API testers available but I was curious if you could integrate them right into your GitHub. I would like it to run automatically whenever a merge would occur rather than having to run an API tester manually.
I am suggesting continuous integration tool which are quite a advanced version of what you want and can do much more than just testing including building binaries, deployment, updating package repositories. Most of them follow a small configuration file which includes listing of dependencies, what to install and commands to run tests (precisely any script that you want to run).
Note: These are free for public repos with some restrictions but you have to pay for private repos and other customisation.