We study a quantum network extending in one dimension (chain of square loops connected at one vertex) made up of quantum wires with Rashba spin-orbit coupling. We show that the Rashba effect may give rise to an electron localization phenomenon similar to the one induced by magnetic field. This localization effect can be attributed to the spin precession due to the Rashba effect. We present results both for the spectral properties of the infinite chain and for linear transport through a finite-size chain connected to leads. Furthermore, we study the effect of disorder on the transport properties of this network.