Yep. As @Its2loud said, the Ring sensors work with Echo routines (not SmartThings routines) and SmartThings virtual devices work with Echo routines, so you can get partial integration that way. Ring sensor alerts, Alexa turns on a virtual ST Switch, you have other ST events react to that switch coming on. You can even create a virtual sensor as a proxy.
It’s easier than the method that requires new code, but it’s still limited.
The following FAQ is intended for the other direction (ST as the trigger), but it’s the same method.
FAQ: Can I trigger an Echo Action without Speaking to It?