  We prove the existence of the set of ground states in a suitable energy space
$\Sigma^s=\{u: \int_{\mathbb{R}^N} \bar{u}(-\Delta+m^2)^s u+V |u|^2<\infty\}$,
$s\in (0,\frac{N}{2})$ for the mass-subcritical nonlinear fractional Hartree
equation with unbounded potentials. As a consequence we obtain, as a priori
result, the orbital stability of the set of standing waves. The main ingredient
is the observation that $\Sigma^s$ is compactly embedded in $L^2$. This enables
us to apply the concentration compactness argument in the works of
Cazenave-Lions and Zhang, namely, relative compactness for any minimizing
sequence in the energy space.
