This paper deals with the measurement of the fluid viscosity by using the torsional vibration of a circular rod excited by a torsional vibrator at one end. The effect of an adjacent viscous fluid on the torsional vibration of the rod has been studied theoretically and expressed in terms of the mechanical impedance. The theoretically-obtained trend that the mechanical impedance is proportional to the square root of the viscosity times the density of the fluid has been confirmed by the impedance measurement. The paper demonstrates that a torsionally-vibrating rod can be used as a sensor to measure the viscosity of a fluid.