  The anisotropic Ginzburg-Landau system \[ \Delta u+\delta\, \nabla
(\mathrm{div}\: u) +\delta\, \mathrm{curl}^*(\mathrm{curl}\: u)=(|u|^2-1) u, \]
for $u\colon\mathbb R^2\to\mathbb R^2$ and $\delta\in (-1,1)$, models the
formation of vortices in liquid crystals. We prove the existence of entire
solutions such that $|u(x)|\to 1$ and $u$ has a prescribed topological degree
$d\leq -1$ as $|x|\to\infty$, for small values of the anisotropy parameter
$|\delta| < \delta_0(d)$. Unlike the isotropic case $\delta=0$, this cannot be
reduced to a one-dimensional radial equation. We obtain these solutions by
minimizing the anisotropic Ginzburg-Landau energy in an appropriate class of
equivariant maps, with respect to a finite symmetry subgroup.
