I am a new student in US with no SSN/ITIN at the moment. I want to apply for unsecured Bank of America credit card and secured capital one and citi/US bank credit cards. But I don't know if I get either unsecured or secured credit cards without having a SSN/ITIN, will they report my activities and will I have my credit history/score like normal(I mean like a person who provided SSN/ITIN when he/she got his/her credit card)?
I doubt you're going to find very many banks in the U.S. that will issue a credit card to anyone without an ITIN or SSN. I did find an article which claims CitiBank might, and I've included the link to it here.
Another option is to become an authorized user on someone else's credit card accounts, although that could be a challenge too without an ITIN or SSN.
Since credit bureaus key their records to SSN or ITIN numbers, it's an open question how you would have a credit bureau file without either one.
Out of curiosity, is there a reason you don't have an ITIN? (maybe you just haven't applied yet?)
Here is the link to the article I mentioned, and hopefully it will give you some ideas on what else you can do: