  We construct vertex operators for massless higher spin fields in RNS
superstring theory and compute some of their three-point correlators,
describing gauge-invariant cubic interactions of the massless higher spins. The
Fierz-Pauli on-shell conditions for the higher spins (including tracelessness
and vanishing divergence) follow from the BRST-invariance conditions for the
vertex operators constructed in this paper. The gauge symmetries of the
massless higher spins emerge as a result of the BRST nontriviality conditions
for these operators, being equivalent to transformations with the traceless
gauge parameter in the Fronsdal's approach. The gauge invariance of the
interaction terms of the higher spins is therefore ensured automatically by
that of the vertex operators in string theory. We develop general algorithm to
compute the cubic interactions of the massless higher spins and use it to
explicitly describe the gauge-invariant interaction of two $s=3$ and one $s=4$
massless particles.
