We have studied the mass currents through a superfluid 3He Josephson weak link in the presence of an externally applied ac pressure modulation. Characteristic changes in the dc mass currents are observed whenever the superfluid Josephson frequency omega(J) is an integer multiple of the ac modulation frequency omega. The measured dependencies of these current changes on ac pressure amplitude are in excellent agreement with theory describing quantum phase dynamics of superfluid 3He weak links. These results establish the superfluid analog of the superconducting Shapiro effect.