  The Edelstein effect provides the purely electrical generation and control of
a homogeneous magnetization in primarily nonmagnetic materials with broken
inversion symmetry. Usually, only the spin density response to an external
electric field is discussed. Here, we report on the electrically induced
magnetization containing spin as well as orbital contributions in the
topological oxide two-dimensional electron gas at the interface between
SrTiO$_3$ and AlO. We find that in this particular system the orbital Edelstein
effect exceeds the spin Edelstein effect by more than one order of magnitude.
The main reason are orbital moments of different magnitude in the
Rashba-like-split band pairs.
