Magnetic moments in an ultra-thin Pt film on a ferrimagnetic insulator Y$_3$Fe$_5$O$_{12}$ (YIG) have been investigated at high magnetic fields and low temperatures by means of X-ray magnetic circular dichroism (XMCD). We observed an XMCD signal due to the magnetic moments in a Pt film at the Pt $L_{3}$- and $L_{2}$-edges. By means of the element-specific magnetometry, we found that the XMCD signal at the Pt $L_{3}$-edge gradually increases with increasing the magnetic field even when the field is much greater than the saturation field of YIG. Importantly, the observed XMCD intensity was found to be much greater than the intensity expected from the Pauli paramagnetism of Pt when the Pt film is attached to YIG. These results imply the emergence of induced paramagnetic moments in Pt on YIG and explain the characteristics of the unconventional Hall effect in Pt/YIG systems.