The possibility of attributing a characteristic size to the neutrino is discussed in the context of the Glashow-Salam-Weinberg model of the electroweak interactions. We define the electroweak radius by means of the νll' scattering amplitude at the one-loop level. This amplitude can be written, in a certain kinematical domain, in terms of only two form factors, which multiply the electromagnetic current and the weak neutral current, respectively. Since the first one does not depend on the properties of the charged lepton l', its derivative gives a suitable measure of the neutrino size. By construction, the electroweak radius so defined is a finite and gauge-independent quantity of the order 10-33 cm2, and it gets contributions from the proper neutrino electromagnetic vertex, from the γ-Z self-energy, and from part of the box diagrams. We also show explicitly the gauge dependence of the first two contributions.