Private credit over GDP seems to be the currently accepted measure of financial development.
Thorsten Beck, Asli Demirgüç-Kunt and Ross Levine (2000) "A New Database on Financial Development and Structure," World Bank Economic Review 14, pp. 597-605, provides such data available on a World Bank webpage.
Used by Ross Levine, Norman Loayza, and Thorsten Beck (2000) “Financial Intermediation and Growth: Causality and Causes” Journal of Monetary Economics, 46, pp. 31-77.
Also used by Aghion, Howitt, and Mayer-Foulkes (2005) and Aghion and Marinescu (2006).
If this measure is used in country fixed effects estimation, it may capture business cycle rather than the degree of financial development.
Rajan and Zingales (1998) prefer using the index of accounting standards by the Center for International Financial Analysis and Research (CIFAR) in 1983 and in 1990 as the measure of financial development. See the fifth column in Table 4 for why.