We have 12v Solenoids, can we use the Rachio 3 system with the current system?
Seems controller itself can function with 12VAC supply, you’ll need to find a new 12V supply to work with your controller. In a recent thread @Ginja has run into issues using a 12V supply with 24V solenoids, but the controller itself appears to work fine. Do keep in mind that you may be limited to half of normally available power (12VA vs original 24VA), but depending on your setup, that may be sufficient.
Besides Ginja’s situation, I’ve not seen, nor tested, Rachio’s operation while underpowered, but it at least seems safe to try, as long as you make sure to use the right 12VAC supply.