Yes you can! Ring has a feature where you can add "Motion Zones" so you still get monitoring, and you have a boundary you set. If someone enters that boundary, you can get an alert and recording! Here is an article below that shows you how to set them up!
[link|https://support.ring.com/hc/en-us/articles/360041248971-Using-Motion-Zones-with-your-Ring-Video-Doorbell-2nd-Generation-|Using Motion Zones with your Video Doorbell (2nd Generation)|new_window=true]
Of course, you will need a Ring protect plan to have the recording feature