I do not understand your question. It may help to rephrase it if this (and other) response does not address your question. My take-away from your inquiry is how a consumer can obtain a credit card without having to disclose his/her SSN to the potential creditor.
Your concern regarding sharing your personal identifying information with others is certainly well taken and understandable. That said, I know of no potential creditor that is going to consider extending credit to you absent access to your credit history, which requires knowledge of your SSN.
To protect yourself, never provide your personal identifying information to an untrusted source, or absent a true necessity. Monitoring your credit report by checking your credit reports and carefully reviewing your account statements as you receive them can also help limit your exposure.
If you absolutely do not want to provide your SSN to a creditor, you can forgo the use of credit and use cash. Unfortunately, this is not a practical, or sometimes possible, option for many; but it's the only way to completely prevent the possibility of a third-party creditor compromising your personal identifying information.
Good luck to you.
NOTE: This Answer does not constitute legal advice. Every case is fact specific. To render a legal opinion, an attorney must engage in a consultation with a prospective client and review any pertinent documents. This communication does not create an attorney-client relationship with Attorney Amy L. Wells or WELLS LAW OFFICE, INC.