The application of advanced enhancement techniques for geophysical anomalies to global gravity (WGM2012) and magnetic (EMAG2) models sheds light on the complex tectonic evolution of the Rio Grande Rise (RGR) in the southern South Atlantic. Long wavelength Bouguer gravity lows indicate a thicker crust beneath of the ridge, whose nature can be related to a microcontinent or an excess of volcanism within the oceanic realm. Recently dredged continental rocks reinforce the hypothesis of a microcontinent or, at least, slivers of continental crust. However, the reserval magnetic pattern of the processed magnetic anomalies provide no evidence of aborted spreading center similar to the well-studied Jan Mayen microcontinent and the surrounding (inactive) Aegir and (active) Kolbeinsey ridges in the North Atlantic Ocean. The reversal magnetic anomalies show a series N-S trending parallel stripes roughly follow the current South American coastline and segmented by E-W oriented oceanic fracture zones (FZs). The magnetic stripes are bended eastwards at the RGR, showing a more complex magnetic pattern similar to that in the Iceland. The aborted Cruzeiro do Sul Rift (CSR) and the Jean Charcot Chain (JCC) are structures that cross the RGR and contribute to the understanding of the tectonic evolution of the South Atlantic Ocean. NW-SE oriented extensive gravity lows and bathymetric valleys, which mark the CSR, are segmented by E-W trending magnetic lineaments related to FZs. This structural configuration suggests that the extensional event, which formed the rift and the seamounts chain, was replaced by strike-slip movements along the FZs. In addition, we constructed a plate kinematic model for the evolution of the RGR based on bathymetric, free-air and Bouguer gravity and magnetic data. Our model comprises five main stages of the RGR formation and evolution between late Cretaceous and Paleocene (ca. 95 - 60 Ma), separated by published seafloor isochrones. The proposed model suggests that the RGR was built at the mid-Atlantic ridge by increased magmatism probably related to the Tristan da Cunha hotspot.