Can a Gemini woman and Aries man get married?

Yes of course! Air signs (which are Aquarius, Gemini, and Libra) are very much compatible with fire signs ( which are Aries, Leo, and Sagittarius)! But be careful each sign is to have an opposite sign, like Aries' opposite is Libra, Saggitarius' opposite is Gemini, and Leo's opposite is Aquarius. Besides anyone can get married to anyone. No one can really stop you!