  We have investigated the effect of a weak magnetic field on momentum
transport in a thermal QCD medium at finite quark chemical potential using a
semiclassical kinetic theory. In the presence of a magnetic field, the momentum
transport coefficients acquire a tensor structure, reflected by the five shear
$\left(\eta_0, \eta_1, \eta_2, \eta_3\right.$ and $\left.\eta_4\right)$ and two
bulk viscous components $\left(\zeta_0\right.$ and $\left. \zeta_1\right)$. The
weak magnetic field removes the degeneracy in the effective mass of flavours,
leading to different masses for the left-handed (L) and right-handed (R) chiral
modes of quarks. The coefficients, $\eta_0, \eta_1$ and $\eta_3$ decrease with
magnetic field in L mode and increase in $\mathrm{R}$ mode, whereas, $\eta_2$
and $\eta_4$ increase in both L and $\mathrm{R}$ mode. The bulk viscous
coefficients, $\zeta_0$ and $\zeta_1$ increase with magnetic field for both L
and R mode. The shear and bulk viscous coefficients positively amplify with
baryon asymmetry.
