We use neutron polarization analysis to study spin excitation anisotropy in the optimally isovalent-doped superconductor BaFe2(As0.7P0.3)2 (Tc=30 K). Different from optimally hole- and electron-doped BaFe2As2, where there is a clear spin excitation anisotropy in the paramagnetic tetragonal state well above Tc, we find no spin excitation anisotropy for energies above 2 meV in the normal state of BaFe2(As0.7P0.3)2. Upon entering the superconducting state, significant spin excitation anisotropy develops at the antiferromagnetic (AF) zone center QAF=(1,0,L=odd), while the magnetic spectrum is isotropic at the zone boundary Q=(1,0,L=even). By comparing the temperature, wave vector, and polarization dependence of the spin excitation anisotropy in BaFe2(As0.7P0.3)2 and hole-doped Ba0.67K0.33Fe2As2 (Tc=38 K), we conclude that such anisotropy arises from spin-orbit coupling and is associated with the nearby AF order and superconductivity.