DNA shows islanders had Polynesian blood, masonry and the existence of sweet potato make it very likely that they either traded with South Americans (Peru) or voyaged there.
I don't care for anthropological theories that discount that possibility. Anything is possible with human willpower. Even the extreme theory that it was seafaring Chinese traders who brought sweet potato to Rapa Nui (I don't believe it, but...) is possible.
What's most interesting, though, is how Rapa Nui destroyed itself, prioritizing its behemoth stone structures so high that the land was deforested and society crumbled. Basically, a parallel of modern Western society in the making.