  We compute the corrections to the orbital Lense-Thirring effect (or
frame-dragging) in the presence of spacetime torsion. We derive the equations
of motion of a test body in the gravitational field of a rotating axisymmetric
massive body, using the parametrized framework of Mao, Tegmark, Guth and Cabi.
We calculate the secular variations of the longitudes of the node and of the
pericenter. We also show how the LAser GEOdynamics Satellites (LAGEOS) can be
used to constrain torsion parameters. We report the experimental constraints
obtained using both the nodes and perigee measurements of the orbital
Lense-Thirring effect. This makes LAGEOS and Gravity Probe B (GPB)
complementary frame-dragging and torsion experiments, since they constrain
three different combinations of torsion parameters.
