Please tell me more
It isn't possible with every CC issuer, but definitely with BoA and Amex, possibly one or two others. I know Discover and Citi are no longer possible (Citi was until recently).
In a nutshell, the process goes like this: the non-U.S. person opens a bank account in the U.S. (no idea if this can be done virtually, everyone I know has done it in person while visiting the U.S.). BoA seems to be the bank of choice, but again, I have no need for this process myself so I never looked into other options.
Then, they open a secured card during the bank account opening with BoA. They use the card monthly for a good 4-6 months to start building credit. Even without a SSN or ITIN, a credit report/profile will still be created and reported based on name, address, DOB.
After the 4-6 months, they have a reasonable starter credit history built up. Then, they approach Amex and apply by phone for one of the entry Amex cards (e.g. no-fee Hilton, no-fee Delta, etc.). It has to be done by phone though, so no referrals or special links, etc. Almost all the people I know have been approved no problem and the ones that haven't always succeeded after giving it more time. Amex is definitely the issuer of choice, but it might be possible with Barclays also.
It's truly that simple (amazingly)!