  Relying on an effective-string approach in which glueballs --- bound states
of pure Yang-Mills theory --- are modelled by closed strings, we give arguments
suggesting that anyonic glueballs, \textit{i.e.} glueballs with arbitrary spin,
may exist in $(2+1)$-$\,$dimensional Yang-Mills theory. We then focus on the
large$\,$-$N_c$ limit of $SU$($N_c$) Yang-Mills theory and show that our model
leads to a mass spectrum in good agreement with lattice data in the scalar
sector, while it predicts the masses and spins of anyonic glueball states.
