I love a man who says he loves me and wants to marry me in the Islamic way. I found out that he is still married legally to a woman and will not divorce her. If I marry him, does that make me a zina? Is this haram?
Zina is an illegal relationship. This means a relationship between two non-married people.
So if there's an Islamic marriage zina is out of question.
According to shari'a a man is allowed to marry up to four women (by Quran 4:3) under the condition that he doesn't do injustice to any of them and threats them all as equal.
After that come a few conditions as stated in the comment:
Is polygamy allowed in your country?
Is the first wife aware that he want's to marry an other woman?
AFAIK he doesn't need her approval but he should let her know. Note that the first wife could have made a condition in her marriage contract that he shouldn't marry any other wife, in that case he must respect the contract.
It is sunnah to make a marriage public.
Note in case you are living in a western country where polygamy is not allowed an Islamic marriage contract could still be set and approved by Muslims even if it won't be legal or valid according the law. This is a difficult and risky case which many scholars advise to avoid. And if one still want to do so the wife which is not a legal wife in front of the law must assure that here rights (inheritance etc.) are still given, if not she should never sign such a contract or accept such a marriage.