Revive - https://github.com/LibreVR/Revive (As of writing, this works with version 2.0.0.13)
Oculus Software - https://www.oculus.com/setup (It doesn't matter which you download, it's all the same software, SKIP the device setup.)

1.) Navigate to C:\Program Files\Revive (or wherever you have installed Revive)
2.) Copy the following files: LibRevive32.dll, ReviveInjector.exe, openvr_api32.dll and xinput\x86\xinput1_3.dll
3.) Paste them into C:\Program Files (x86)\Steam\steamapps\common\DiRT Rally (or wherever you installed DiRT Rally).
4.) Run the game!

That is it, honestly. You may need to right-click on DiRT Rally in Steam, go to Properties, and disable the VR Theatre checkbox if you're having issues.

You will not enter actual VR until you're at the starting line, so do not be alarmed. The game should start in a greyish theatre (the oculus one, not the SteamVR one).

The game does not support tracked motion controllers.

Even for VR veterans, playing this in VR can make you feel very ill. If you're a beginner, DO NOT PLAY THIS IN VR. And whoever you are, if you do plan on playing it this way, make sure to stop when you begin to feel sick, DO NOT FORCE YOURSELF. Make sure to take a long break if you feel sick, return to it when all your symptoms are gone, and then try again. Eventually you will build up a tolerance, but do not try to "power through it".