  We examine the existence and stability of nonlinear discrete vortex solitons
in a square lattice when the standard discrete Laplacian is replaced by a
fractional version. This creates a new, effective site-energy term, and a
coupling among sites, whose range depends on the value of the fractional
exponent $\alpha$, becoming effectively long-range at small $\alpha$ values. At
long-distance, it can be shown that this coupling decreases faster than
exponential: $\sim \exp(- |{\bf n}|)/\sqrt{|\bf{n}|}$. In general, we observe
that the stability domain of the discrete vortex solitons is extended to lower
power levels, as the $\alpha$ coefficient diminishes, independently of their
topological charge and/or pattern distribution.
