With the usual caveat that this will only work with the classic app, and the classic app will be going away sometime, here’s the discussion thread on possible integrations with the ring alarm system. You need strong technical skills for this.
Also, to clarify what I said above, although abode has an IFTTT channel, and ring has one for their doorbells, they do not have one for their security system and they have already said they are not planning on an open API.
There are some people who are taking advantage of the email feature to send an email from ring alarm to the IFTTT gmail channel. Unlike regular email, the Gmail channel has more options and gets processed much quicker.
Not sure how much Integration you can get that way, but there are some people using it.