Digital holographic microscopy provides new facilities for contactless and marker-free quantitative phase contrast imaging. In this work, a digital holographic microscopy method for the integral refractive index determination of living single cells in cell culture medium is presented. Further, the obtained refractive index information is applied to full field thickness and shape determination of adherent pancreas tumor cells, as well as for analysis of drug-induced dynamic changes of a single cell's cytoskeleton. The results demonstrate that digital holographic microscopy is a quantitative phase contrast technique for living cells under conventional laboratory conditions.