Given an object of mass m and arbitrary shape, its radius of gyration with respect to a fixed axis is the number [tex]r_{g}[/tex] so that the moment of inertia "I" of that object with respect to that axis can be written:
[tex]I=mr_{g}^{2}[/tex]
Assuming you've got a way to measure applied torque and angular acceleration, the object's radius of gyration can be determined experimentally.