  We present a theory of magnetic response in a finite-size two-dimensional
superconductors with Rashba spin-orbit coupling. The interplay between the
latter and an in-plane Zeeman field leads on the one hand to an out-of-plane
spin polarization which accumulates at the edges of the sample over the
superconducting coherence length, and on the other hand, to circulating
supercurrents decaying away from the edge over a macroscopic scale. In a long
finite stripe of width W both, the spin polarization and the currents,
contribute to the total magnetic moment induced at the stripe ends. These two
contributions scale with W and W2 respectively, such that for sufficiently
large samples it can be detected by current magnetometry techniques.
