A new kind of plasma diagnostics, geodesic acoustic mode (GAM) spectroscopy, is proposed. Radial eigenmodes of GAMs with discrete eigenfrequencies in toroidal plasmas are analysed. The eigenmode has a wavelength of the order of (ρi the ion gyroradius, LT the temperature gradient scale length) and has the highest peak near the radius where the eigenfrequency coincides with the local GAM frequency. Therefore, observing the radial position of the highest peak of the eigenmode provides a method to measure the local ion sound velocity. A novel method to measure the ion composition is given, combined with densities and temperatures.