A descending plume in a rotating two-layer stratified ambient fluid is investigated experimentally. The source buoyancy flux of the plume is set to be small so that the mean density of the plume impinging the interface is less than the lower layer density, characterized by a buoyancy parameter, Lambda, being less than unity. In such cases, the discharged plume fluid spreads radially at the interface in the form of an intrusive gravity current at early times. At later times, this intrusion evolves to form an anticyclonic lens due to the influence of the Coriolis force. The measured radial position of the intrusion front, R(t), follows a power law relationship against time, t, that transitions from the early time gravity current regime for which the power law exponent lies between 0.5 and 1.1 to late times when the intrusion acts as a rotationally influenced expanding lens for which the power law exponent ranges between 0.15 and 0.5, with generally smaller values for larger Lambda. The plume fluid reaching the interface progressively increases in density due to re-entraining relatively dense fluid as the plume descends within the lens. Consequently, the plume eventually penetrates through the interface and descends to the bottom of the tank. Faster rotation makes the lens thicker and hence increases the volume of the re-entrained lens-fluid, which decreases the time for the onset of penetration. The penetration time normalized by the rotation rate is found to hold a simple power law relationship with Lambda.