An arc-electrode capacitive sensor has been developed for quantitative characterization of permittivity of cylindrical dielectric rods. The material property of the cylindrical test piece can be inversely determined from the sensor output capacitance based on a theoretical model. For the modeling process, the electrostatic Green’s function due to a point source exterior to a dielectric rod is derived. The sensor output capacitance is numerically calculated using the method of moments (MoM), in which the integral equation is set up based on the electrostatic Green’s function. Numerical calculations on sensor configuration optimization are performed. Calculations also demonstrate the quantitative relationship between the sensor output capacitance and the test-piece dielectric and structural properties. Capacitance measurements on different dielectric rods with different sensor configurations have been performed to verify the validity of the numerical model. Very good agreement (to within 3%) between theoretical calculations and measurement results is observed.