Can ginger tea induce periods if so how soon?

No, but: Ginger tea is fine to drink, if one enjoys the ginger flavor. Avoid using too much sugar, or too much of other sweeteners. It won't change one's menstrual periods, which means that any change in one's menstrual periods after drinking ginger tea is actually a coincidence and not caused by ginger tea. If periods are truly altered by the tea, there's more than just ginger in there (scary thought!).