Yes, it would cause that. Magnesium plays an essential role in the functioning of cells, tissues and organs throughout people's body. It would cause muscles twitches in the eyelid if you do not intake enough magnesium, other factors, such as smoking, drinking alcohol could cause eye twitch as well. You also could experience symptoms such as fatigue, vomiting, nausea when you do not have adequate magnesium supplement. An eyelid twitch does not typically indicate a serious condition. It just notices that you should pay attention to your diet or lifestyle, which would disappear within a day. You can find rich magnesium from almonds, bananas, milk, lima beans.