Is it possible to do PhD in Computational Social Science without CS background?
Based on your question and your comments (this and that), I do think you need to take more math and statistics before you apply for PhD. I don't think MOOC courses, such as Linear Algebra and Statistics with R are enough for you to be considered qualified to get into good Computational Social Science programs (You didn't even taken Calculus).

I would suggest you to apply for an MS in computer science first. Once you receive formal and rigorous math and CS trainings, then you apply for  Computational Social Science PhD programs. You will have much better chance to get in first or second tier schools this way.