  The magnetic insulator $\alpha$-RuCl$_{3}$ is a promising candidate to
realize Kitaev interactions on a quasi-2D honeycomb lattice. We perform
extensive susceptibility measurements on single crystals of
$\alpha$-RuCl$_{3}$, including angle-dependence of the in-plane longitudinal
and transverse susceptibilities, which reveal a unidirectional anisotropy
within the honeycomb plane. By comparing the experimental results to a
high-temperature expansion of a Kitaev-Heisenberg-$\Gamma$ spin Hamiltonian
with bond anisotropy, we find excellent agreement with the observed phase shift
and periodicity of the angle-resolved susceptibilities. Within this model, we
show that the pronounced difference between in-plane and out-of-plane
susceptibilities as well as the finite transverse susceptibility are rooted in
strong symmetric off-diagonal $\Gamma$ spin exchange. The $\Gamma$ couplings
and relationships between other terms in the model Hamiltonian are quantified
by extracting relevant Curie-Weiss intercepts from the experimental data.
