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 interfer-
ometer 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
