The regulations don't actually mandate a specific rim diameter for the wheels, however it is often mentioned that F1 uses 13 inch diameter rims. Having looked at some images of wheels and tyres and taking measurements, I'm lead to believe the rim size is actually around 14 inches.
I've been working on a scale drawing of an F1 car and noticed a problem with the scale of the wheel rim diameter to tyre diameter. I had been using the front wheel from the following image as a placeholder. When I compared the tyre diameter to wheel rim diameter, it transpired that the wheel had a relative scale of around 16.5 inches, which is far to big for F1:
I compared a few more images of wheels and tyres such as the following on the Mercedes W06. These both gave a wheel rim diameter of almost 14.2 inches:
The following image of the Williams FW16 gave a wheel rim diameter of 14.8 inches: