Excitons in two-dimensional (2D) semiconductors have offered an attractive platform for optoelectronic and valleytronic devices. Further realizations of correlated phases of excitons promise device concepts not possible in the single particle picture. Here we report tunable exciton spin orders in WSe2/WS2 moiré superlattices. We find evidence of an in-plane (xy) order of exciton spin-here, valley pseudospin-around exciton filling vex = 1, which strongly suppresses the out-of-plane spin polarization. Upon increasing vex or applying a small magnetic field of ~10 mT, it transitions into an out-of-plane ferromagnetic (FM-z) spin order that spontaneously enhances the spin polarization, i.e., the circular helicity of emission light is higher than the excitation. The phase diagram is qualitatively captured by a spin-1/2 Bose-Hubbard model and is distinct from the fermion case. Our study paves the way for engineering exotic phases of matter from correlated spinor bosons, opening the door to a host of unconventional quantum devices.