We propose a mechanism of angular momentum conversion from optical transverse spin in surface plasmon polaritons (SPPs) to conduction electron spin. Free electrons in the metal follow the transversally spinning electric field of SPP, and the resulting orbital motions create inhomogeneous static magnetisation in the metal. By solving the spin diffusion equation in the SPP, we find that the magnetisation field generates an electron spin current. We show that there exists a resonant condition where the spin current is resonantly enhanced, and the polarisation of the spin current is flipped. Our theory reveals a novel functionality of SPP as a spin current source.