  Magnetic anisotropy of spin models with directional-dependent interactions in
the high-temperature paramagnetic phase is theoretically studied. Using a high
temperature expansion, we show that the Ising type directional-dependent
interaction gives rise to magnetic anisotropy which depends on the temperature
as $\propto T^{-5}$. This phenomenon arises from the anisotropic exchange
interaction, and is distinct from the orbital effect, such as van Vleck
susceptibility. It is shown that while the quadratic term in the magnetization
favors to point the spins along the bond, the fourth order term in
magnetization prefers to point spins to the perpendicular direction. The theory
is applied to the Heisenberg-Kitaev model on the honeycomb lattice and a cubic
lattice model that is potentially relevant to perovskite iridates. We show
that, in these models, the anisotropic terms in quadratic order cancels out,
and the leading order for the magnetic anisotropy arises from the fourth order
contribution. The result shows that the anisotropy from the
directional-dependent interaction gives rise to $\langle100\rangle$ magnetic
anisotropy. These results are potentially relevant to heavy transition metal
oxides such as iridates. Experimental observation of the magnitude of
anisotropic interactions using magnetic torque measurement is also discussed.
