Despite intense studies the exact nature of the order parameter in superconducting Sr2RuO4 remains unresolved. We have used small-angle neutron scattering to study the vortex lattice in Sr2RuO4 with the field applied close to the basal plane, taking advantage of the transverse magnetization. We measured the intrinsic superconducting anisotropy between the c axis and the Ru-O basal plane (similar to 60), which greatly exceeds the upper critical field anisotropy (similar to 20). Our result imposes significant constraints on possible models of triplet pairing in Sr2RuO4 and raises questions concerning the direction of the zero spin projection axis.