Only a few efforts have been made to design small scatterers with special polarimetric properties. In this article, the possibility of designing a planar single-layer resonant scatterer presenting roll invariant cross polarization is demonstrated for the first time. The invariance condition for a general scatterer is first derived analytically from the scattering matrix for co and cross polarization. Then a design method for a resonant scatterer made from two dipoles with unique angular and phase arrangement is presented. The first step of the design is done theoretically using field superposition. The effects of the coupling between the dipoles and the finite ground plane size are taken into account in a second step by simulation. Two scatterers operating at 4.26 GHz and 5.26 GHz have been manufactured and measured providing good performance with a relative variation of their cross polarization component lower than-2 dB and-2.7 dB respectively. Finally, the scattering matrix corresponding to the current design is compared with other classical targets.