I’m confused here, are you asking for something that joins a group on button click, or are you looking for something that accepts them to a group?
If you’re asking for someone to click a button and it automatically joins your group, that won’t be possible unless they provide you there .ROBLOSECURITY cookie and a few other things, which I don’t think is reasonable for someone to ask for.
To my knowledge, Noblox doesn’t have a functionality to actually join a group. You could go the route of when you press the button, it sends to repl.it and then that makes a request to Groups api, but you’ll run into issues with captchas doing that.
FWIW: if you can afford to wait, Open Cloud should support group management APIs in the future so you wouldn’t need a cookie to get this done. You would just need to set up a credential that has access to the groups API and then execute your requests there. No telling how far off that is though.