Although many of the major credit card companies won't give you a card without a credit history, some smaller ones, like department stores, will. Find a department store that will issue you a card and apply for it. You can try getting a gas station card also. Either way, use your card but be sure to make all payments on time. Your goal is to build a good credit history, not just get a credit card.
Find a credit card company that will review your overall financial situation and not just your credit history. Some lenders will look at your employment history, your housing situation, and how often you have moved. If this is all on the up and up, they may approve your application. Again, use this card wisely.