  We analyze a semi-discrete splitting method for conservation laws driven by a
semilinear noise term. Making use of fractional $BV$ estimates, we show that
the splitting method produces a compact sequence of approximate solutions
converging to the exact solution, as the time step $\Delta t \rightarrow 0$.
Under the assumption of a homogenous noise function, and thus the availability
of $BV$ estimates, we provide an $L^1$ error estimate. Bringing into play a
generalization of Kruzkov's entropy condition, permitting the "Kruzkov
constants" to be Malliavin differentiable random variables, we establish an
$L^1$ convergence rate of order $\frac13$ in $\Delta t$.
