  Theory of the electron spin relaxation in graphene on the SiO$_2$ substrate
is developed. Charged impurities and polar optical surface phonons in the
substrate induce an effective random Bychkov-Rashba-like spin-orbit coupling
field which leads to spin relaxation by the D'yakonov-Perel' mechanism.
Analytical estimates and Monte Carlo simulations show that the corresponding
spin relaxation times are between micro- to milliseconds, being only weakly
temperature dependent. It is also argued that the presence of adatoms on
graphene can lead to spin lifetimes shorter than nanoseconds.
