  By using the momentum-space Lanczos recursive method which considers
rigorously all multiple-scattering events, we unveil that the non-perturbative
disorder effect has dramatic impact on the charge transport of a
two-dimensional electron system with Rashba spin-orbit coupling in the
low-density region. Our simulations find a power-law dependence of the dc
longitudinal conductivity on the carrier density, with the exponent linearly
dependent on the Rashba spin-orbit strength but independent of the disorder
strength. Therefore, the classical charge transport influenced by complicated
multiple-scattering processes also shows the characteristic feature of the
spin-orbit coupling. This highly unconventional behavior is argued to be
observable in systems with tunable carrier density and Rashba splitting, such
as the LaAlO$_{3}$/SrTiO$_{3}$ interface, the heterostructure of Rashba
semiconductors bismuth tellurohalides and the surface alloy
Bi$_x$Pb$_y$Sb$_{1-x-y}$/Ag(111).
