It has only been a few days since the release of the Droid RAZR and already the developer community has figured out a way to root the phone. The method below is for WINDOWS only and is taken from Droidforums

Rooting voids your warranty. Not following the instructionscarefullymight result in a bricked phone. Proceed at your own risk!

Step 1:Download and install Motorola Drivers for your Windows PC (this doesn’t work on other operating systems):32-bitor64-bit.

Step 2:DownloadDooMLoRD_v2_ROOT-zergRush-busybox-su.zipand extract contents to your PC (desktop would be a good place).

Step 3:From your Droid RAZR’s homescreen, tapMenubutton and enableUSB DebuggingfromSettings > Applications > Development.

Step 4:Connect your Droid RAZR with your PC and selectCharge Onlyoption from notifications drawer.

Step 5:Navigate to where the folder you unzipped in Step 2 to and open the folder and click on therunme.batfile and let it do its thing.

You only need to do this process once.