I couldn't find any up-to-date answer, and thats why I am making new question.
Is the facebook page like URL still around? For example, there used to be a way to get only the like URL of your Facebook page, so when some user clicks that link, they automatically will like your page.
Is that still possible?
If not, then how can I make an option for my page to be like through my Android game?
As I just tested, the facebook like url is still working. try this https://www.facebook.com/plugins/like.php?href=http://facebook.com/duckseason.mobi
of cource replace the final facebook.com/.... with your facebook page
On Android I think you could add it inside a webview and place the webview inside a layout inside your game. If the device is connected to the internet it should work fine. I do not know how it will handle the facebook connection though