La0.67Sr0.33MnO3 (LSMO) thin films under compressive strain have an orthorhombic symmetry with (1-10)o and (001)o in-plane orientations. (The subscript o denotes the orthorhombic symmetry.) Here, we grew LSMO on cubic (LaAlO3)0.3-(Sr2AlTaO6)0.7 (LSAT) substrates and observed a uniaxial contribution to the magnetic anisotropy which is related to the orthorhombic crystal structure. Since the lattice mismatch is equal in the two directions, the general understanding of anisotropy in LSMO, which relates the uniaxial anisotropy to differences in strain, cannot explain the results. These findings suggest that the oxygen octahedra rotations associated with the orthorhombic structure, possibly resulting in different Mn-O-Mn bond angles and therefore a change in magnetic coupling between the [1-10]o and [001]o directions, determine the anisotropy. We expect these findings to lead to a better understanding of the microscopic origin of the magnetocrystalline anisotropy in LSMO.