As you want the List of Universities provide Doctorates in Social Work I am giving here the same.
List of Some of the Universities that provide PhD programs and/or Professional Doctorates in social work:

University of Toronto
York University
University of Calgary
University of Melbourne
University of Sydney
University of Windsor
Carleton University
McMaster University
Tallinn University
Finnish National University Network for Social Work
Bournemouth University
Cardiff University
University of East London (via The Tavistock and Portman NHS Foundation Trust)
Norwegian University of Science and Technology
University of Gothenburg
Umea University
University of Edinburgh
Keele University
Goldsmiths, University of London
University of Manchester
Aurora University
Adelphi University
University of California, Berkeley
University of California, Los Angeles
School of Social Work (Rutgers University)
University of Portsmouth
University of Southampton
University of York
University at Buffalo, The State University of New York
University of Michigan
University of Pennsylvania
Columbia University
New York University
University of Connecticut
Fordham University, the Jesuit University of New York
University of Pittsburgh
University of Iowa
Barry University
University of Houston
University of Maryland
University of Missouri
University of South Carolina
University of Illinois
University of Texas
University of Kansas
University of Utah
Capella University
University of Denver
University of Tennessee
University of Alabama
Indiana University