  We report measurements of the normal state in-plane magnetoconductance in
gated LaAlO$_3$-SrTiO$_3$ samples. As the orientation of the magnetic field
changes within the plane of the interface, the signal displays periodic
oscillations with respect to the angle between the field and the direction of
the current. We show that in the underdoped to optimally doped range, a Fermi
surface reconstruction takes place due to the Rashba spin-orbit term and that
the oscillations are due to a magnetic field induced opening and closing of a
gap at the $\Gamma$ point for those Ti out-of-plane orbitals having their band
minimum close to the Fermi energy of the system.
