I haven’t done this specific thing, but I’ve ton a ton of things like it.
It’s definitely possible via the group.MemberJoined webhook event (US docs).
In Zapier, you use Webhooks by Zapier - catch a hook action - as your trigger. You then have to subscribe the URL they give you (when you get to testing the trigger) to the webhook. I use Postman to do that subscription. From there, when the event happens, it sends the payload data to the webhook, which Zapier catches the data.
Next, you can use the pre-built Zapier action to assign points and/or take other steps before/after.
One similar use case I use is the webhook event for marking an answer. I’ve added a 10 point incentive for users to mark an answer to their question, as that type of action helps focus attention on the questions that still need answers and reduces moderation needs.