  Dynamical multiferroicity features entangled dynamic orders: fluctuating
electric dipoles induce magnetization. Hence, the material with paraelectric
fluctuations can develop magnetic signatures if dynamically driven. We identify
the paraelectric KTaO$_3$ (KTO) as a prime candidate for the observation of the
dynamical multiferroicity. We show that when a KTO sample is exposed to a
circularly polarized laser pulse, the dynamically induced ionic magnetic
moments are of the order of 5\% of the nuclear magneton per unit cell. We
determine the phonon spectrum using ab initio methods and identify T$_{1u}$ as
relevant soft phonon modes that couple to the external field and induce
magnetic polarization. We also predict a corresponding electron effect for the
dynamically induced magnetic moment which is enhanced by several orders of
magnitude due to the significant mass difference between electron and ionic
nucleus.
