  We calculate the Dirac neutrino anapole moment (a_{\nu_l}) in the context of
the Standard Model (SM) making use of the Dirac form factor F_D(q^2) introduced
recently by J. Bernabeu, L. G. Cabral-Rosetti, J. Papavassiliou y J. Vidal by
using the Pinch Technique (PT) formalism, working in two different gauge-fixing
schemes (R_\xi guage and the electroweak BFM), at the one loop level. We show
that the neutrino anapole form factor F_A(q^2) and Dirac form factor F_D(q^2)
are related as follows: F_A(q^2) = \frac{1}{q^2} F_D(q^2). Hence, the Dirac
neutrino charge radius < r^2_{\nu_l} > and the anapole moment satisfy the
simple relation a_{\nu_l} = {1/6} < r^2_{\nu_l} >. Therefore, we show that the
anapole moment (as the charge radius) of the neutrino is a physical quantity,
which only gets contribution from the proper neutrino electromagnetic vertex
(in electroweak BFM), and that a_{\nu_l} is of the order 10^{-34} cm^2.
