Very good question @F50! If DHCP is disabled on your router, and you do not want to use a DHCP reservation, you can certainly use a static IP or select a private IP address. The IP address would of course still need to be within your subnet (I.E. between 192.168.0.2 - 192.168.0.255).
Once you have an IP address in mind, begin a new setup in the Ring app, and tap “add a hidden network” when you get to the last step of “selecting your home wifi network”. You will see the “add a hidden network” option will give you the ability to manually enter your network info, including IP address. Hope this helps!