My answer for this is as follows:
There is a thing called a secured credit card.. you simply put the required deposit down, and then the credit card company should give you a credit card..

Or.. if you can show your bank that you've got more than enough money/investments to cover a credit card limit, then they will probably give you a credit card. My son did this on his 18th birthday. He had more than enough in his savings and the bank didn't even require him to have a security deposit or co-signor.

I really encourage people to have more than enough savings in their account before getting their first credit card.. If you're just starting off and don't have any savings then you're likely to run into trouble with payments. You'll be using the credit card as an income source, rather that a convenience tool that needs to be repaid each month.

It takes a while to save up the money, but that's really the best way to go.
Patience and credit cards are a good policy

This question was asked on:
Can I get a secured credit card eventhough I don't have a credit history?
http://answers.yahoo.com/question/index?qid=20100203182546AAuJIzr