We have investigated the critical current I-c of intrinsic Josephson junctions (IJJs) in Co/Au/Bi2Sr2CaCu2Oy mesa structures as a function of magnetic field. The current-voltage characteristics of the mesas before a magnetization of Co layer showed the multiple quasiparticle branches with hysteresis similar to that of conventional IJJs. On the other hand, the magnetic field dependence of I-c clearly showed hysteretic behavior different from that of conventional IJJs. It is found that such dependence corresponds to the magnetization curve of the Co layer and the I-c has a maximum at the coercive field of the Co layer. The observed modulation of I-c of the Co/Au/Bi2Sr2CaCu2Oy mesa is attributed to the injection of the spin-polarized current.