There are accounts about the use of the sling by the indians when they fought against the Spaniards. So I think that the first settlers carry slings with them when they crossed the Bering Strait from Asia.
When Columbus discovered America
When the Spanish began colonizing America would meet again with the sling, now managed, among other weapons, with great skill by the natives. Since Cortes, when he enters the city of Mexico and makes Moztezuma prisoner has to endure harassment by the sling well of the long and dreadful darts thrown with "tiraderas" (atlatl).
In fact, Moztezuna, who had been disowned by his people because of their weakness to the Spanish, dies sling a stone thrown from a distance, and he sank half of the temple.
But it will Pizarro, in his brilliant conquest of Peru, which will have the opportunity to appreciate the importance that the Incas were in a sling, his weapon of choice in the fight from a distance. Huayna Capac the Inca king, according to a written tradition, went to war on a litter from red to sling projectile fired his gold.
In general, all used the Andean sling and rich in references to the chroniclers of the conquest of their effectiveness in the hands of the Indians. One of these writers relates to sling a stone could kill a horse and break into two long and robust Spanish swords.
http://perso.wanadoo.es/hondero/temas.htm Greetings.