Some data to that effect has come forth from the genetic study of sweet potato herbarium spécimens brought back by James Cook expedition (Source: Switek, 2013). These strongly suggest that sweet potato was introduced to Oceania from South America around 1000 AD. There are also suggestions that similarities in the term to designate sweet potatoes in Quechua (kumara) and Polynesia (kuumala) might be the result of some kind of cultural contact. It is however not possible to completely rule out that these sweet potatoes were naturally dispersed westward by winds and currents, or that their seeds were carried by birds, or some such.

There was some suggestion that chicken bones on Mocha Island showed polynesians made it to the Chilean coast, but genetic analysis strongly suggests they are genetically distinct from polynesian chickens (Source: Thompson et al., 2014).

There are also strong suggestions of some kind of direct genetic exchange between Easter Islanders and South Americans some time around 1500's, but the age estrimate on that is quite coarse (Source: Lawler, 2014).

That being said, there are no written records of such contact or exchanges. To my knowledge all evidence suggesting such contact is genetic, or possibly archeological. They add up to tantalising hints and credible suggestions, but it has not been formally proven.