We use polarized neutron scattering to demonstrate that in-plane spin excitations in electron doped superconducting BaFe1.904Ni0.096As2 (Tc=19.8 K) change from isotropic to anisotropic in the tetragonal phase well above the antiferromagnetic (AFM) ordering and tetragonal-to-orthorhombic lattice distortion temperatures (TN≈Ts=33±2 K) without an uniaxial pressure. While the anisotropic spin excitations are not sensitive to the AFM order and tetragonal-to-orthorhombic lattice distortion, superconductivity induces further anisotropy for spin excitations along the [110] and [110] directions. These results indicate that the spin excitation anisotropy is a probe of the electronic anisotropy or orbital ordering in the tetragonal phase of iron pnictides.