BERLIN—An Austrian appeals court has decided that a Inc. can be tried in Austria, overturning a regional court’s rejection of the case and adding to the headwinds the social network is already facing in Europe.

Maximilian Schrems lodged a complaint in 2013 against Facebook over alleged privacy violations, claiming the company’s data-use policy was invalid under European Union law. A regional court in Vienna rejected his complaint in the summer, saying it didn’t have jurisdiction for the case. The higher court decided this...