Card sorting can be a quantitative or qualitative research method.
Common goals when carrying out a card sorting study include: learning what users think about an existing IA, understanding why users group ideas in certain ways, and discovering how users categorize information.
These results could be qualitative, e.g. participant commentary during a moderated session, or they could be quantitative, e.g. statistics on time to complete the test, number of cards sorted, or percentage of cards in one group.