  Centrosymmetric antiferromagnetic semiconductors, although abundant in
nature, seem less promising than ferromagnets and ferroelectrics for practical
applications in semiconductor spintronics. As a matter of fact, the lack of
spontaneous polarization and magnetization hinders the efficient utilization of
electronic spin in these materials. Here, we propose a paradigm to harness
electronic spin in centrosymmetric antiferromagnets via Zeeman spin splittings
of electronic energy levels -- termed as spin Zeeman effect -- which is
controlled by electric field.By symmetry analysis, we identify twenty-one
centrosymmetric antiferromagnetic point groups that accommodate such a spin
Zeeman effect. We further predict by first-principles that two
antiferromagnetic semiconductors, Fe$_2$TeO$_6$ and SrFe$_2$S$_2$O, are
excellent candidates showcasing Zeeman splittings as large as $\sim$55 and
$\sim$30 meV, respectively, induced by an electric field of 6 MV/cm. Moreover,
the electronic spin magnetization associated to the splitting energy levels can
be switched by reversing the electric field. Our work thus sheds light on the
electric-field control of electronic spin in antiferromagnets, which broadens
the scope of application of centrosymmetric antiferromagnetic semiconductors.
