Unfortunately, the Ring Alarm system can only currently activate the sirens on the Alarm Base Station, and Keypads, and the indoor non-weather-resistant Dome Siren. 
But you aren’t alone in wanting an external siren! Many others want an outdoor weather-resistant siren, or some ability to connect an exterior siren, or some way to have a siren sound outdoors . The more “Thumbs Up” Kudo votes they see there will better get their attention, increasing the chances of getting siren sounds outdoors. You should click the related links below and add your Kudo vote, if you like the requesting author’s idea (add your “Thumbs Up” Kudo vote on the left side of the author’s starting post), to help get the attention of the Ring Teams.
Submitted by Hamster1 :
https://community.ring.com/t5/Feature-Request-Board/External-Siren/idi-p/67621
Submitted by DrTej and several others (similar requests merged into this request):
Submitted by Jayfalcon22 :
https://community.ring.com/t5/Feature-Request-Board/Link-Siren/idi-p/64706
Submitted by Brumey :
Submitted by Paul209 :
https://community.ring.com/t5/Feature-Request-Board/Alarm-camera-siren-integration/idi-p/69879
Submitted by abc :
Submitted by Doug_in_Calgary :
Submitted by THESPEC1ALONE :
https://community.ring.com/t5/Feature-Request-Board/External-alarm/idi-p/36839