  In this paper we prequantize the moduli space of non-abelian vortices. We
explicitly calculate the symplectic form arising from the $L^2$ metric and we
construct a prequantum line bundle whose curvature is proportional to this
symplectic form. The prequantum line bundle turns out to be Quillen's
determinant line bundle with a modified Quillen metric. Next, as in the case of
abelian vortices, we construct Quillen line bundles over the moduli space whose
curvatures form a family of symplectic forms which are parametrised by
$\Psi_0$, a section of a certain bundle.
