Yes. There is no law that prohibits a debtor from opening a bank account after filing bankruptcy. However, if you owed money to a bank (i.e. for a credit card, loan, overdraft fees, etc.) and they were included in your bankruptcy, chances are you might have a difficult time opening an account with that institution.
You may need to shop around in order to find a bank that is willing to open a new account.
Prior to filing bankruptcy, if you have an account with a bank that you owe money to, your attorney may recommend that you close that account and open a new account at a bank where you have not borrowed funds or owe money. Generally speaking, it is best to open a new bank account before you file bankruptcy to ensure that you have a bank account with an institution who you do not owe money to.