  We demonstrate that the spin orientation of an electron propagating in a
one-dimensional nanostructure with Rashba spin-orbit (SO) coupling can be
manipulated on demand by changing the geometry of the nanosystem. Shape
deformations that result in a non-uniform curvature give rise to complex
three-dimensional spin textures in space. We employ the paradigmatic example of
an elliptically deformed quantum ring to unveil the way to get an
all-geometrical and all-electrical control of the spin orientation. The
resulting spin textures exhibit a tunable topological character with windings
around the radial and the out-of-plane directions. We show that these
topologically non trivial spin patterns affect the spin interference effect in
the deformed ring, thereby resulting in different geometry-driven ballistic
electronic transport behaviors. Our results establish a deep connection between
electronic spin textures, spin transport and the nanoscale shape of the system.
