The relative intensity noise (RIN) of a semiconductor laser subject to partially coherent optical feedback has been studied both theoretically and experimentally. Good agreement between theory and experiment is obtained, but only if the optical feedback is considered to be partially coherent. At low bias currents there is an almost linear increase in the RIN with optical feedback strength, until stable external cavity operation is obtained. For higher bias currents the behaviour is similar to that of the coherent optical feedback case, except that there is now a local minimum in the RIN within the coherence collapse regime.