It is not impossible to get a credit card with bad credit and if you look around you will see that there are a lot of credit card companie out there. The first thing to remember is to not run around applying to multitudes of credit card companies, hoping that one will give you a credit card, because all the application rejections can damage your credit even further.
Don't give anyone money who promises that they can get you a credit card either, because these are almost always scams. Be strategic and move slowly is what is going to work best.
One method that has worked for some people is to go get a simple business license from the county you live in and then create some quick company stationary that has you as the president on the letter head and send off a nice letter in it with your application that explains your circumstances in a positive light.
Be careful not to get to liberal with your optimism as it can cross over into bank fraud. You can easily get a business license for a fencing company, or any one of a number of trades that don't require that you pass a state contractors exam. The cost of a license like this is usually between fifty and one-hundred dollars.
Don't bother applying to any of the more recognized credit card names because they are going to reject you out right if you have bad credit and no collateral. The off brand credit card names are your best bet in this case and the card you will receive will have a relatively low credit limit but it is a start. After you get the credit card make sure that you make your payments promptly and start working on improving your credit.