DISCLAIMER: Droid Forums or myself will not be responsible if you happen to brick your device during this root process. Please 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-bit or 64-bit.
Step 2: Download DooMLoRD_v2_ROOT-zergRush-busybox-su.zip and extract contents to your PC (desktop would be a good place).
Step 3: From your Droid RAZR’s homescreen, tap Menu button and enable USB Debugging from Settings > Applications > Development.
Step 4: Connect your Droid RAZR with your PC and select Charge Only option from notifications drawer.
Step 5: Navigate to where the folder you unzipped in Step 2 to and open the folder and click on the runme.bat file and let it do its thing.
If you followed the steps correctly, your Droid RAZR should now be rooted on Android 2.3.5 Gingerbread.
Thanks to Pieman13 for the find!