The air fluorescence telescopes are one essential part of the Pierre Auger Project, currently under construction in Argentina. With a pixel camera of 440 photomultiplier tubes the telescopes observe fluorescence light induced by cosmic ray extensive air showers passing through the atmosphere. In this paper we report on a method to monitor the dc anode current in each photomultiplier by statistical analysis of the signal fluctuations. The method has in our case the advantage that we were able to implement it using free resources of FPGA logic; therefore no additional electronics is required. We present details of the current monitor design and its performance measured with a prototype device.