H-4 visa holders can’t get a social security number. They cannot open a separate bank account or get a credit card without Social Security Number. They can share a joint account with their spouse and also, a joint credit card/debit card.
A social security number is required to run a credit check. As H-4 visa holders do not have a financial presence in the U.S., they don’t have a credit history.
(09.25.07) An important correction: H4 Visa holders can open a bank account individually -it has to be a checking and not savings.
Thanks for your input Kiah!