Resistive Plates Chambers (RPC) are detectors biased at High-Voltage (HV) in excess of 4kV. When fired by a particle, they develop a large signal current that can be read across a small resistance, 100Ω or so. A characterization has been made of their ageing as a function of the behaviour of their leakage current with time. An array of 10 detectors has been developed for this purpose. We present the instrument designed and built to perform a continuous and automatic monitoring of the leakage current from each detector of the array, while the system is taking data. For the particular biasing set-up adopted, the current has been measured in series to the terminal connected to the HV of every channel. Since the small value of the currents, order of tens of nA, a special circuit solution and special precautions have been adopted.