We have investigated the atomic structure of superconducting Ca-intercalated bilayer graphene on a SiC(0001) substrate using total-reflection high-energy positron diffraction. By comparing the experimental rocking-curves with ones calculated for various structural models using a full-dynamical theory, we have found that Ca atoms are intercalated in the graphene-buffer interlayer, rather than between the two graphene layers. From transport measurements, the superconducting transition was observed to be at Tc_onset = 4K for this structure. This study is the first to clearly identify the relation between the atomic arrangement and superconductivity in Ca-intercalated bilayer graphene.