The effect of Rashba spin-orbit coupling on the spin interference in a noninteracting one-dimensional ring connected to two leads is studied theoretically within the nonequilibrium Greens' function formalism. We compute the charge and spin currents and analyze their Aharonov-Bohm oscillations. The geometry of the system is conveniently described by the angle δ between the two leads. We show that for δ=180°(i.e., for symmetrically coupled leads), a good filtering of up- or down-spin orientation is obtained around half-integer multiples of Φ/ Φ0. These particular flux values are degeneracy points for clockwise and counterclockwise propagating states, corresponding to the same spin orientation in the local spin frame of the ring. In contrast, for the asymmetric coupling, i.e., δ=135°, the filter efficiency is maximum around integer multiples of Φ/ Φ0. The numerical results suggest that the spin filtering is obtained when the clockwise or counterclockwise states interfere destructively. It turns out that the spin filtering regime is stable against variations in the bias applied on the system. The quasiperiodic oscillations of the charge current, as a function of the Rashba strength, are obtained and discussed.