  We demonstrate that fractional cubic-quintic nonlinear Schr\"odinger
equation,characterized by its L\'evy index, maintains ring-shaped soliton
clusters ("necklaces") carrying orbital angular momentum. They can be built, in
the respective optical setting, as circular chains of fundamental solitons
linked by a vortical phase field. We predict semi-analytically that the
metastable necklace-shaped clusters persist, corresponding to a local minimum
of an effective potential of interaction between adjacent solitons in the
cluster. Systematic simulations corroborate that the clusters stay robust over
extremely large propagation distances, even in the presence of strong random
perturbations.
