  Dominant multi-particle interactions can give rise to exotic physical phases
with anyonic excitations and phase transitions without local order parameters.
In spin systems with a global $SU(N)$ symmetry, cyclic ring-exchange couplings
constitute the first higher-order interaction in this class. In this letter we
propose a protocol how $SU(N)$ invariant multi-body interactions can be
implemented in optical tweezer arrays. We utilize the flexibility to re-arrange
the tweezer configuration on time scales short compared to the typical
lifetimes, in combination with strong non-local Rydberg interactions. As a
specific example we demonstrate how a chiral cyclic ring-exchange Hamiltonian
can be implemented in a two-leg ladder geometry. We study its phase diagram
using DMRG simulations and identify phases with dominant vector chirality, a
ferromagnet, and an emergent spin-$1$ Haldane phase. We also discuss how the
proposed protocol can be utilized to implement the strongly frustrated $J-Q$
model, a candidate for hosting a deconfined quantum critical point.
