  We investigate the possibility of spin texture in the bilayer cuprate
superconductor $\rm Bi_2Sr_2CaCu_2O_{8+\delta}$ using cluster dynamical mean
field theory (CDMFT). The one-band Hubbard model with a small interlayer
hopping and a Rashba spin-orbit coupling is used to describe the material. The
$d$-wave order parameter is not much affected by the presence of the Rashba
coupling, but a small triplet component appears. We find a spin texture
circulating in the same direction around $\mathbf{k}=(0,0)$ and
$\mathbf{k}=(\pi,\pi)$ and stable against the superconducting phase. The
amplitude of the spin structure, however, is strongly affected by the pseudogap
phenomenon, more so than the spectral function itself.
