Persistent spin textures (PST) are special spin configurations in spin-orbit-coupled systems in which spin polarization acquires a symmetry-enforced momentum-independent orientation, leading to exceptionally long spin lifetimes and persistent spin helices. However, identifying direct experimental probes for PST, remains challenging because conventional quantum-geometric responses are strongly suppressed in this regime. Here, we show that PST systems isolate spin-rotation quantum geometry, which manifests through distinctive nonlinear magnetotransport responses. Using both a fine-tuned Rashba-Dresselhaus two-dimensional electron gas model and a candidate material Ge${}_3$Pb${}_5$O${}_{11}$ with symmetry-enforced cubic spin-splitting realizing PST, we demonstrate that PST suppresses conventional and Zeeman quantum-geometric contributions, leaving the spin-rotation quantum geometric tensor as the sole source of nonlinear magnetic-current and spin-magnetization responses. Remarkably, the nonvanishing response components exhibit identical direction-independent behavior as a function of chemical potential, providing a distinctive signature of PST. We further show that, in the Rashba-Dresselhaus two-dimensional electron gas at the PST point, these qualitative signatures remain robust even in the presence of a cubic Dresselhaus term that breaks the exact SU(2) symmetry. Our results establish nonlinear magnetotransport as an experimentally accessible probe of PST and their underlying spin-rotation quantum geometry.