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The spin-orbit coupling (SOC) in the 5d iridates gives rise to a large variety of quantum phases such as J_eff=1/2 Mott insulating state. Due to the entanglement of spin and orbital degrees of freedom, the form of magnetic interactions depends closely on the underlying lattice geometry and could lead to novel magnetic ground states, for example, the weak ferromagnetism in the square lattice Sr₂IrO₄ with 180-degree Ir-O-Ir bond angle and proximity to the Kitaev model in the honeycomb lattice Na₂IrO₃ with 90-degree bond angle. We report neutron and x-ray diffraction studies of the magnetic order of the triangle lattice Ca₂Sr₂IrO₆. In this system, individual Ir ions are well separated from each other and form nearly undistorted IrO₆ octahedron. An antiferromagnetic order is observed below 13 K, with magnetic configuration breaking the 3-fold symmetry of the triangle lattice. The ordering moment is about 0.6 µ_B/site, larger than those of other iridates with strong connectivity between neighboring Ir ions. The anisotropic magnetic behavior highlights the important role of SOC in determining the magnetic ground state in this triangle lattice iridate.