That’s the sticky situation.
First of all before you start credit card shopping, request your credit score. It is always better to know exact numbers then grope in the dark. Besides you can check it for any inaccuracies.
Now let’s see what you can do. You may apply for a regular credit card but for this you may need a checking account. If you do have a checking account, look through bad credit section. Some offers may appear right for you.
If you don’t have checking account take a look at Credit One Bank credit card. This is an unsecured credit card, so you don’t need a deposit.
And the last, think on your situation little bit more. If you say that you don’t have start up sum for a security deposit, then will it be good for you to apply for a credit card again? May be it is worth waiting for a while. Regain strength, get more educated, and pave the way to your future financial stability.