Is it possible to find a PhD position in social sciences without having letters of recommendation?
It really does not matter where you come from. In general, to apply for a PhD program in the U.S., you need: application letter, resume, reference letters (usually 3), master's degree (mostly required), transcripts from bachelor's and master's program, and GRE score (many programs require it). In addition, TOEFL score if your native language is not English.

Most of the time, if you are admitted to a PhD program in social sciences, you will be granted with assistantship / scholarship at the same time. Mostly, it's an assistantship, which means you will teach or do something else for the department. The stipend of the assistantship usually is only enough for you to live, not for your research study. If you need funding for your research study, you have to invest your own savings, or get research funding from the department or other grant institutions, which is not easy to get.

For the resources, use Google or Google Scholar to look for related publications or scholars. Actually, it is a good strategy to contact professors for the research topic first. If a professor is interested in your research topic or finds you competent during the discussion, it will increase the possibility for the professor to accept you to his/her program. But, be carefully prepared, don't send email before digging into the literature.