  The Milky Way is expected to be embedded in a halo of dark matter particles,
with the highest density in the central region, and decreasing density with the
halo-centric radius. Dark matter might be indirectly detectable at Earth
through a flux of stable particles generated in dark matter annihilations and
peaked in the direction of the Galactic Center. We present a search for an
excess flux of muon (anti-) neutrinos from dark matter annihilation in the
Galactic Center using the cubic-kilometer-sized IceCube neutrino detector at
the South Pole. There, the Galactic Center is always seen above the horizon.
Thus, new and dedicated veto techniques against atmospheric muons are required
to make the southern hemisphere accessible for IceCube. We used 319.7 live-days
of data from IceCube operating in its 79-string configuration during 2010 and
2011. No neutrino excess was found and the final result is compatible with the
background. We present upper limits on the self-annihilation cross-section,
$\left<\sigma_\mathrm{A} v\right>$, for WIMP masses ranging from 30 GeV up to
10 TeV, assuming cuspy (NFW) and flat-cored (Burkert) dark matter halo
profiles, reaching down to $\simeq 4 \cdot 10^{-24}$ cm$^3$ s$^{-1}$, and
$\simeq 2.6 \cdot 10^{-23}$ cm$^3$ s$^{-1}$ for the $\nu\overline{\nu}$
channel, respectively.
