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?
Yes, although having a background that involves computing methods (ex. computer science, GIS, statistics, etc.) will make you a stronger candidate.
Computational Social Science is still a very new field. If you look at the CV's of the big names in the discipline very few of them come from a computer science background. It is much more common to see things like geography (Crooks), physics (Grimm), political science (Axelrod, Epstein), and sociology (Carley, Gilbert). Most of the methods in computational social science are not extremely complex to code so computer science skills are not really a barrier to entry.
As always, the best way to resolve the question is to reach out the universities and departments you are looking to study with. Very few universities are offering the degree and George Mason is the only really big name program I can think of off the top of my head. They prefer that student come from either a computer science or a social sciences background which generally seems to be the trend. You may also want to look into various social sciences departments to see if they have anyone interested in computational social science since they might be able to guide you to a PhD in Social Science using computational social science methods.