Relocated to USA. How to get credit card without existing credit history / score?

Secured credit cards are usually not very cost effective for building credit. Find a local credit union, of medium to large size. A credit union is like a bank, but operates under slightly different rules, and is non-profit. Locally based credit unions often have more flexibility when it comes to offering you loans and credit. If you just need a card that you can use for daily and online purchases, get a debit card from your credit union. Most CU's will offer a small personal line of credit to protect you from overdraft and overdraft fees when using the debit card. This will not build much credit, but it can help protect you from accidents when using the debit card. To have a good credit score, you need a long history of paying loans on-time. A great way to build credit long term is through cash-secured loans from your local credit union. You essentially take out a loan against your own money. You can typically set up automatic payments, so you never miss a payment deadline. The loan term (length of time to pay it off) should be fairly long, so that more history is built. One of the best ways to build credit is getting a mortgage & paying it on-time, every month. With little credit history, you won't get a good interest rate on that mortgage, at first. Once you have built a better score, refinance the mortgage for a better rate, better terms, etc. Once again: go to a local credit union, they can help you navigate most of this.

Most banks will give you a credit card if you open an account with sufficient funds. It especially helps if you have have a job that direct deposits into your account.

I think your options are to get a secured card like you said or possibly get a credit card from a local bank that you can build a relationship with. Sometimes local banks are more willing to work with you as a person instead of the National Banks that look at you like an account number.

If you have had an American Express card abroad, you can try and get a US Amex on the strength of it, otherwise you're looking at a secured card if you really want a credit card. That's basically what I did. Of course the downside with Amex is that it's not accepted everywhere. I'm not a big fan of people co-signing for credit cards (or loans for that matter). I'd also talk to the local credit union(s) and see what they have available.

If the country you came from has an HSBC, you can ask HSBC to use your credit rating from that country to give you an HSBC Mastercard in the US. This might only be a service for HSBC Premier but it's worth checking. I moved from UK to US and got $10,000 credit limit immediately based on my UK credit rating.

My local bank (on which I had had my pay direct-deposited for a while when I applied) rejected me for a credit card, but a major national institution accepted me after an online application. I had expected the opposite, but this is what happened. I got a tiny amount of credit at first and had to be careful for a while not to go over the limit, but I immediately set up "automatic full payment" from my checking account and started getting automatic increases regularly. It only takes a year or so to have a very good score if you use your card and always pay it in full. This was before the new "consumer protection" laws when it was easier to get credit, so you might have to get a secured card. It might be a $25 investment or so, but if you ever get a real loan (like a mortgage or even for a car) it's more than worth it. Even just the cashback you'll get once you upgrade to a real card will pay back those $25 fast. Also, it might depend on how it's set up, but being an authorised user on someone else's account might not contribute to your history.

If you have family or friends in the US, you can ask them to add you as an additional card holder on their credit card account. I have done it for a friend, and he was able to obtain his own credit card after a year on my card. Otherwise, look for a http://cufind.com/ that will be a bit more flexible than a bank.