Two issues:

1. Planck length The resolution of the circle would be too low to be precisely pi. (I'm not sure whether everything moves only in Planck lengths or whether we live in a voxel world but either way it's not as precise as however many digits of pi we know.
2. Matter waves Assuming that the circle has energy (which it must due to Heisenberg's uncertainty principle(I haven't actually read this but I assume that like a vacuum according to the unruh effect matter can't be devoid of energy)) the particles making up that circle would have a wavelength in which they can interfere with other particles and also have an area in which they might be.