You could, in theory, obtain a size for the pinhole by very precisely measuring the *brightness* of the image it casts compared to the brightness of the light source used. I have a hunch, however, that you'd get a diameter (after considerable effort and calculation) that was only good to about plus or minus 10%, at best (few light meters are better than 1/3 stop on accuracy).

You should also be able to obtain a diameter by shining a coherent light through the hole (like a laser pointer) and projecting the image far enough to see the ring-shaped diffraction pattern, and then measuring the diameter of the first ring and distance from pinhole to screen. This ought to be a very accurate method, if you know the wavelength of the laser (not too hard to obtain, as they come in a limited number of choices) and are certain you're measuring the first diffraction ring outside the central peak. I'd expect this to require a projection distance of something like 100 times the "optimum" for imaging, in order to spread the diffraction pattern enough to be easy to measure -- so for a hole around 1/100 inch diameter, you'd need to project it about 16+ feet.