The antiferromagnetic compound Ba(TiO)Cu4(PO4)4 contains square cupola of corner-sharing CuO4 plaquettes, which were proposed to form effective quadrupolar order. To identify the magnetic structure, we have performed spherical neutron polarimetry measurements. Based on symmetry analysis and careful measurements, we conclude that the orientation of the Cu2+ spins form a noncollinear in-out structure with spins approximately perpendicular to the CuO4 motif. Strong Dzyaloshinskii-Moriya interaction naturally lends itself to explain this phenomenon. The identification of the ground-state magnetic structure should serve well for future theoretical and experimental studies into this and closely related compounds.