Usually, banks that have international branches accept ITIN numbers.
I usually recommend that you go with an international branch and create an account with them at your home branch to make the process of opening a US bank account a little easier.
As of this writing, all the following banks accept ITINs.
If you don’t have your ITIN yet, you will not be able to open a US bank account without one.
If you need an ITIN, apply for your ITIN on this page.
Bank of America
Bank of America generally will allow a bank account to be opened without a Social Security Number (SSN). However, you will have to provide two pieces of identification, which can be your ITIN and passport.
Additionally, they’ll also need you to provide your proof of address in the US.
According to NerdWallet, with this information, you should be able to open a Bank of America Awards Savings Account.
The only drawback to opening a bank account with them is that you’ll have to go into the branch to do it.