The Shulhan Aruch (Orah Haim 183:5) cites an opinion that if a left-handed person is reciting Birkat Ha’mazon over a cup of wine, he holds the cup in his left hand. However, the view of the Kabbalists, as brought by the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) in Parashat Hukat, is that even left-handed people should hold the cup of wine with their right hand. And, as noted by Hacham Ovadia Yosef, the Shulhan Aruch himself rules that on Sukkot, a left-handed person holds the Lulab in the right hand, just like right-handed people. Therefore, the correct practice is for a left-handed person to hold the cup of wine in his right hand.
Summary: A left-handed person who recites Birkat Ha’mazon over a cup of wine holds the cup in his right hand, just like a right-handed person.
Daily Halacha
With What Hand Does a Left-Handed Person Hold the Cup of Wine During Birkat Ha-mazon?
Lectured by Rabbi Eli Mansour