Magnetoresistance of a semiconducting ferromagnetic nanostructure with a laterally constrained domain wall is analyzed theoretically in the limit of sharp domain walls and fully polarized electron gas is considered. The spin-orbit interaction of Rashba type is included into considerations. It is shown that the magnetoresistance in such a case can be relatively large, which is in a qualitative agreement with recent experimental observations. It is also shown that spin-orbit interaction can enhance the magnetoresistance. The role of localization corrections is also briefly discussed.