Künkler is co-PI of the Iran Social Science Data Portal. She is co-editor of the Cambridge Journal of Law and Religion and Brill Research Perspectives in Religion and Politics, a member of the editorial boards of the Journal for the Scientific Study of Religion (Wiley), the International Journal of Islam in Asia (Brill), the Digest of Middle East Studies (Wiley) and Iranian Studies (Cambridge). She is chair of the Scientific Advisory Council for the Centre for Global Cooperation Research, University of Duisburg, and a member of the Scientific Advisory Committee for “Les Femmes Politiques” of the Association Tunisienne de la Psychologie de la Santé. In the past, she has been a fellow of the “Women Creating Change” Project on Gender, Religion, and Law in Muslim Societies at Columbia University, New York, NY, a fellow of the project “Confronting the Governance Crisis in the MENA” funded by the Carnegie Corporation, and a Senior Consultant to the project “Islamic Authority in the Middle East” at Rice University, funded by the Henry Luce Foundation. She is a former Member of the MESA Committee on Academic Freedom and President-Elect of the Association for the Study of Persianate Societies (ASPS).

Beside her permanent posts, Künkler has held fellowships and visiting professorships at the Faculty of Social Science, University of Tehran, Iran; the Centre for Strategic and International Studies, Jakarta; the Islamic State University (UIN), Alauddin Makassar (Sulawesi), Indonesia; the Institut Michel Villey at Université Paris II Panthéon-Assas; the International Institute for the Sociology of Law (IISJ), Spain; the Wissenschaftszentrum Berlin (WZB); the Politics Department at the University of Oxford; the Center for Interdisciplinary Research (ZIF) in Bielefeld where she was co-PI for a six-month research group on Constitutionalism and Religion; and the Royal Netherlands Institute of Southeast Asian and Caribbean Studies (Koninklijk Instituut voor Taal-, Land- en Volkenkunde, KITLV).