We English speakers say ON THE MENU. If you were to say in the menu, you would not be wrong, just would get strange looks and people would take you for a foreigner.

Think of it this way instead: If it is being displayed on its surface, it is ON. If it is found within the object, it is IN. "You look silly on that photo" "Donuts are on the shelf" "I am sitting on the couch" "What's on the menu?" "What's on TV?" "I am in Tokyo" "Donuts are in the fridge" "It's in your mind" "It is in there" "What's in your car?" (This explains both why things are on menus, or on electronic devices)

Both are OK. You could say it is in the menu because it is listed next to various other dishes. On the menu is OK as it could be on a notice board as the dish of the day for instance.

it is ON the menu. because this phrase refers to the food listed ON the menu