  The magnetic structure of honeycomb iridate Na$_2$IrO$_3$ is of paramount
importance to its exotic properties. The magnetic order is established
experimentally to be zigzag antiferromagnetic. However, the previous assignment
of ordered moment to the $\bm{a}$-axis is tentative. We examine the magnetic
structure of Na$_{2}$IrO$_{3}$ using first-principles methods. Our calculations
reveal that total energy is minimized when the zigzag antiferromagnetic order
is magnetized along $\bm{g}\approx\bm{a}+\bm{c}$. Such a magnetic configuration
is explained by adding anisotropic interactions to the nearest-neighbor
Kitaev-Heisenberg model. Spin-wave spectrum is also calculated, where the
calculated spin gap of $10.4$ meV can in principle be measured by future
inelastic neutron scattering experiments. Finally we emphasize that our
proposal is consistent with all known experimental evidence, including the most
relevant resonant x-ray magnetic scattering measurements [X. Liu \emph{et al.}
{Phys. Rev. B} \textbf{83}, 220403(R) (2011)].
