When could I apply for a credit card?

Once your bankruptcy case is filed, you have the ability to apply for and acquire a credit card.  Lenders have gotten pretty aggressive these days with soliciting people after filing a bankruptcy for credit.  One of the reasons why creditors do this is that they know that you cannot file another fresh start Chapter 7 bankruptcy case for eight years from the date of filing your current case.  Plus, the creditor is hoping that you will use the card, pay the annual fee, pay late fees, pay interest fees and basically go into the same bad habits that might have gotten you into debt in the first place.  The creditors are not offering you credit because they want to help you.  They are offering you credit because they want to make money from you, they want you to use their card because they make money whether or not you just use the card and pay off the balance or whether or not you incur additional fees, late fees and carry a balance.  Obviously, they make more money with the latter; however, if they can just get you using the card, they get a certain percentage from the merchants.  So you have the ability to apply for a card and acquire a card immediately after a Chapter 7 bankruptcy case.
Now, in some cases, you might want to get a secured credit card.  That is where you are putting a certain dollar amount; say $250 or $500 in a bank account and that is what you have for charging privileges.  You are basically not getting credit but you are using your own down payment security deposit or credit as your ability to charge.  The good thing about a secured credit card is those cards can turn into unsecured credit cards shortly down the road, provided you continue to make current payments.
So yes, you can acquire a credit card immediately after filing and you will get offers for credit cards very shortly after filing.