  We study the possibility of realizing topological phases in graphene with
randomly distributed adsorbates. When graphene is subjected to periodically
distributed adatoms, the enhanced spin-orbit couplings can result in various
topological phases. However, at certain adatom coverages, the intervalley
scattering renders the system a trivial insulator. By employing a finite-size
scaling approach and Landauer-B\"{u}ttiker formula, we show that the
randomization of adatom distribution greatly weakens the intervalley
scattering, but plays a negligible role in spin-orbit couplings. Consequently,
such a randomization turns graphene from a trivial insulator into a topological
state.
