We study the spin states of a few-electron quantum dot defined in a two-dimensional electron gas, by applying a large in-plane magnetic field. We observe the Zeeman splitting of the two-electron spin triplet states. Also, the one-electron Zeeman splitting is clearly resolved at both the zero-to-one and the one-to-two electron transition. Since the spin of the electrons transmitted through the dot is opposite at these two transitions, this device can be employed as an electrically tunable, bipolar spin filter. Calculations and measurements show that higher-order tunnel processes and spin-orbit interaction have a negligible effect on the polarization.