We establish theoretically that transverse spin textures are generically induced by the spin-orbit interaction at the Fermi surface of centrosymmetric ferromagnetic metals. We confirm this prediction with em ab initio computations for Fe, Co and Ni. By symmetry, this cannot be associated with spin-orbit torques under a uniform current. However, a new em current-gradient-induced torque emerges in nanoscale geometries. For a series of Ni-based bilayers, the computed Ni thickness dependence of the current-gradient-induced torque is in quantitative agreement with measurements previously attributed to orbital torques. We discuss how this opens a new avenue for the electrical control of magnetic orders, possibly also including the Néel vector of metallic altermagnets.