  We study the electrical transport properties of a two-dimensional electron
gas with the Rashba spin-orbit interaction in presence of a constant
perpendicular magnetic field $(B_0 \hat z)$ which is weakly modulated by ${\bf
B_1} = B_1 \cos (q x) \hat z$, where $B_1 \ll B_0 $ and $q = 2 \pi/a $ with $a$
is the modulation period. We obtain the analytical expressions of the diffusive
conductivities for spin-up and spin-down electrons. The conductivities for
spin-up and spin-down electrons oscillate with different frequencies and
produce beating patterns in the amplitude of the Weiss and Shubnikov-de Haas
oscillations. We show that the Rashba strength can be determined by analyzing
the beating pattern in the Weiss oscillation. We find a simple equation which
determines the Rashba spin-orbit interaction strength if the number of Weiss
oscillations between any two successive nodes is known from the experiment. We
compare our results with the electrically modulated 2DEG with the Rashba
interaction. For completeness, we also study the beating pattern formation in
the collisional and the Hall conductivities.
