We review the General Relativity induced precession of a spin of relativistic particles in storage rings in terrestrial environment. Besides the clasical geodetic effect there emerges a spin rotation
in focusing fields needed to compensate for the Earth gravity force acting on stored particles. The both effects have a structure of the spin-orbit interaction in the Earth gravitational field. Our major
point is a vindication of the 2012 Orlov-Flanagan-Semertzidis derivation of the GR induced false EDM signal in the all-electric frozen-spin rings. The experimental observation of the GR signal
would serve as an important indicator of a performance of a storage ring. We also comment on the GR effect in a hybrid $\overrightarrow{E}$x$\overrightarrow{B}$ ring envisioned by the CPEDM Collaboration.