  A rotating interferometer with paths that enclose a physical area exhibits a
phase shift proportional to this area and to the rotation rate of the frame.
Understanding the origin of this so-called Sagnac effect has played a key role
in the establishment of the theory of relativity and has pushed for the
development of precision optical interferometers.The fundamental importance of
the Sagnac effect motivated the realization of experiments to test its validity
for waves beyond optical, but precision measurements remained a challenge.Here
we report the accurate test of the Sagnac effect for matter waves, by using a
Cesium-atom interferometer featuring a geometrical area of 11 cm$^2$ and two
sensitive axes of measurements. We measure the phase shift induced by the
Earth's rotation and find agreement with the theoretical prediction at an
accuracy level of 25 ppm. Beyond the importance for fundamental physics, our
work opens practical applications in seismology and geodesy.
