  We present here the proposal to use the LISA interferometer for detecting the
gravito-magnetic field due to the rotation of the Milky Way, including the
contribution given by the dark matter halo. The galactic signal would be
superposed to the gravitomagnetic field of the Sun. The technique to be used is
based on the asymmetric propagation of light along the closed contour of the
space interferometer (Sagnac-like approach). Both principle and practical
aspects of the proposed experiment are discussed. The strategy for
disentangling the sought for signal from the kinematic terms due to proper
rotation and orbital motion is based on the time modulation of the time of
flight asymmetry. Such modulation will be originated by the annual oscillation
of the plane of the interferometer with respect to the galactic plane. Also the
effect of the gravitomagnetic field on the polarization of the electromagnetic
signals is presented as an in principle detectable phenomenon.
