As a generalization of semi-invariant submersions, we introduce conformal semi-invariant submersions from almost product Riemannian manifolds onto Riemannian manifolds. We give examples, and investigate the geometry of foliations which arise from the definition of a conformal submersion and show that there are certain product structures on the total space of a conformal semi-invariant submersion. Moreover, we also find necessary and sufficient conditions for a conformal semi-invariant submersion to be totally geodesic.