We show that a femtosecond spin-current pulse can generate terahertz (THz) transients at Rashba interfaces between two nonmagnetic materials. Our results unambiguously demonstrate the importance of the interface in this conversion process that we interpret in terms of the inverse Rashba Edelstein effect, in contrast to the THz emission in the bulk conversion process via the inverse spin-Hall effect. Furthermore, we show that at Rashba interfaces the THz-field amplitude can be controlled by the helicity of the light. The optical generation of electric photocurrents by these interfacial effects in the femtosecond regime will open up new opportunities in ultrafast spintronics.