It would be better if you applied for a secured credit card but since you don’t want to pay a deposit you have not so many options. And most of the offers will be shopping credit cards which can be used at particular retailers for shopping and nothing else. The rest of them will be prepaid cards, which are not good for you because they do not report to credit bureaus. All these offers you can see on bad credit cards page. Think over secured credit cards again. The deposit you will have to pay is usually fully refundable and will be paid when you close your account. Besides you don’t have to pay more to increase the initial credit limit. To have timely payments and stay within limits will be enough for credit limit increase.