Is there an expression to describe a poor woman who marries a rich man for money?
Solution 1:
Gold digger is the usual term for somebody who pursues a relationship for money. Its connotation is more greed than poverty, however. If you want a more neutral term, I'd suggest marriage of convenience.
Solution 2:
Consider hypergamy
(colloquially referred to as "marrying up") is the act or practice of marrying a spouse of higher caste or status than oneself.
The term does not specifically refer to money, but social class or caste and money are very closely related.