  Motivated by the recent discovery of high temperature antiferromagnet
SrRu$_2$O$_6$ and its potential to be the parent of a new superconductor, we
construct a minimal $t_{2g}$-orbital model on a honeycomb lattice to simulate
its low energy band structure. Local Coulomb interaction is taken into account
through both random phase approximation and mean field theory. Experimentally
observed Antiferromagnetic order is obtained in both approximations. In
addition, our theory predicts that the magnetic moments on three
$t_{2g}$-orbitals are non-collinear as a result of the strong spin-orbit
coupling of Ru atoms.
