The measurement of a very low intensity of an electric current is carried out by 5 integrating the electric current over integration cycles having a time period ti and measuring a peak value of a sawtooth voltage at an integrated circuit output each time at the end of the integration cycle, whereat noise voltage components of a frequency above a cut-off frequency, which has a value of the order of magnitude (0,1×2π×ti)−1, being parts of a voltage of a noise generated in an operational amplifier comprised in the integrated circuit are filtered out of the said sawtooth voltage and noise components, which have the origin in the high-frequency voltage components of Johnson noise, which appear in the low-frequency spectral part of the sawtooth voltage as aliasing, are subtracted from a filtered sawtooth voltage. A higher absolute accuracy of the measurement is achieved by means of a reduction of the direct as well as the aliasing contribution of the Johnson noise of the operational amplifier in the measuring circuit.