  We investigate spin relaxation in rippled graphene where curvature induces a
Zeeman-like spin-orbit coupling with opposite effective magnetic fields along
the graphene plane in ${\bf K}$ and ${\bf K}^\prime$ valleys. The joint effect
of this Zeeman-like spin-orbit coupling and the intervalley electron-optical
phonon scattering opens a spin relaxation channel, which manifests itself in
low-mobility samples with the electron mean free path being smaller than the
ripple size. Due to this spin relaxation channel, with the increase of
temperature, the relaxation time for spins perpendicular to the effective
magnetic field first decreases and then increases, with a minimum of several
hundred picoseconds around room temperature. However, the spin relaxation along
the effective magnetic field is determined by the curvature-induced Rashba-type
spin-orbit coupling, leading to a temperature-insensitive spin relaxation time
of the order of microseconds. Therefore, the in-plane spin relaxation in
low-mobility rippled graphene is anisotropic. Nevertheless, in the presence of
a small perpendicular magnetic field, as usually applied in the Hanle spin
precession measurement, the anisotropy of spin relaxation is strongly
suppressed.
