In general neutron stars in binaries are spinning. Recently, a new quasi-equilibrium approximation that includes a rotational velocity piece for each star has been proposed to describe binary neutron stars with arbitrary rotation states in quasi-circular orbits. We have implemented this approximation numerically for the first time, to generate initial data for neutron star binaries with spin. If we choose the rotational velocity piece such that it equals the Newtonian rigid rotation law, we obtain stars with fluid 4-velocities that have expansion and shear of approximately zero, as one would expect for quasi-equilibrium configurations. We also use the new approach to construct and study initial data sequences for irrotational, corotating and fixed rotation binaries.