I am a Dutch citizen, currently residing in the Netherlands. I have no credit history but I do have a US social security number, as I have worked in the US some time ago.
I have a checking account with Bank of America.

I want a US credit card, as I regularly rent a car in the US and want to save on insurance.

I tried applying for a credit card online with Bank of America using the US address of a very close friend of mine. I had to lie about being a permanent resident to have the application even go through. I got denied as I have no credit history.

What to do?

I don't care what kind of APR the card has as I'm not planning to put anything on it. I just want to use it when renting a car and paying in cash when I return the car.

Anyone got a good idea?

Consider getting a secured card like Orchard bank's Secured. It will cost you a little bit per year, but you will establish a credit history and also you'll be eligible for an upgrade after 6-12 months.