Is it possible to do PhD in Computational Social Science without CS background? As the title states, I don't have Computer Science background (B.A. in Business Administration and Master of Social Work) but would like to do PhD in Computational Social Science (Data analysis or Information sci).

There are master programs, mostly professional programs, admit students from whole range of areas, such as Computational Analytics and Public Policy from U of Chicago or QMSS from Columbia. 

But PhD programs don't. Although PhD programs state on their website that they accept students regardless of their backgrounds, it means that they accept students from mathematics, statistics, or linguistics, but not from Social Work.

My interest is solving social issues by using computational approach. I have taken MOOC courses, such as Linear Algebra and Statistics with R, and I learned R and Python(both intermediate). I also have been working as RA in ICT in Bangladesh project.

To me, it becomes clearer that what PhD programs want is those who have solid CS knowledge and the idea of doing PhD seems to be so unrealistic.

Is it really impossible to do PhD in Data Sci or Info Sci without direct/indirect CS knowledge? If it is possible what should I do?
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.