To end up in the Americas you'd first have to catch the Canary current. It's not certain that the Romans went that far south, although the Periplus Hannonis att

To end up in the Americas you'd first have to catch the Canary current. It's not certain that the Romans went that far south, although the Periplus Hannonis attests that a Carthaginian expedition sailed as far as Mount Cameroon. From the Periplus Maris Erythraei we know that the India trade was well established in Roman times, but crossing the Arabian Sea and crossing the Atlantic are two different things. One you can do in a dhow, the other not so much.