This Ohio State University thesis paper tries to answer this exact question:
James McGann, Director of the Think Tanks and Civil Societies Program at the Foreign Policy Research Institute, defines think tanks as “public policy research, analysis, and engagement institutions.” Until recently, McGann did not consider the World Bank a think tank because of its relationship with rich governments. In 2009, McGann ranked the World Bank Institute, a division within the Bank, among the top think tanks worldwide. McGann does not consider other research branches of the World Bank think tanks. However, the Development Economics Vice Presidency, known as DEC, is the central research arm of the Bank and exemplifies all think tank characteristics.
Overall, after analyzing the different departments within the Bank and their research, it is evident that the World Bank goes beyond McGann’s definition. Last year the Bank spent $750 million on “knowledge,” or research, and in 2009 it was top-ranked among research institutions on development. The World Bank’s budget for research has declined significantly since a 2006 evaluation report, which ironically recommended just the opposite. Nations and donors should recognize the need for the World Bank to sustain the research budget in order to support the work and knowledge produced by DEC and the other research-intensive departments. This will continue the Bank’s role as a super think tank on global development and public policy advocacy.Indeed, in the latest University of Pennsylvania think tank ratings, the World Bank Institute (WBI) is ranked as the #3 best government-affiliated think tank, behind Congressional Research Service (CRS) at #1 and the German Institute for International and Security Affairs (GIISA) at #2. WBI has about 200 staffers, or about the same size as many of the larger Washington think tanks. A 2006 figure says that the DEC has 80 full-time staffers, 15 "other long-term researchers," and 30 support staff.
By comparison, the Commerce Department, which also has myriad economists but is not a think tank, has around 43,880 employees. The Congressional Research Service (CRS), the top government-affiliated think tank, has a staff of around 675.
Many think tanks also attract former World Bank staffers. Although I haven't done a full count yet, I know that myriad World Bankers reside at Brookings and the Peterson Institute for International Economics (PIIE).
In addition, the World Bank does its own work with think tanks. Recently, it has written about and sponsored several workshops and conferences related to think tanks in developing countries.