[en] The core rotation rates of massive stars have a substantial impact on the nature of core-collapse (CC) supernovae and their compact remnants. We demonstrate that internal gravity waves (IGWs), excited via envelope convection during a red supergiant phase or during vigorous late time burning phases, can have a significant impact on the rotation rate of the pre-SN core. In typical ($10M_{\odot <!--\; ???\; -->}\lesssim <!--\; ???\; -->M\lesssim <!--\; ???\; -->20M_{\odot <!--\; ???\; -->}$) supernova progenitors, IGWs may substantially spin down the core, leading to iron core rotation periods $P_{\mathrm{m}\mathrm{i}\mathrm{n},\mathrm{F}\mathrm{e}}\gtrsim <!--\; ???\; -->30\mathrm{s}$. Angular momentum (AM) conservation during the supernova would entail minimum NS rotation periods of $P_{\mathrm{m}\mathrm{i}\mathrm{n},\mathrm{N}\mathrm{S}}\gtrsim <!--\; ???\; -->3\mathrm{m}\mathrm{s}$. In most cases, the combined effects of magnetic torques and IGW AM transport likely lead to substantially longer rotation periods. However, the stochastic influx of AM delivered by IGWs during shell burning phases inevitably spin up a slowly rotating stellar core, leading to a maximum possible core rotation period. We estimate maximum iron core rotation periods of $P_{\mathrm{m}\mathrm{a}\mathrm{x},\mathrm{F}\mathrm{e}}\lesssim <!--\; ???\; -->5\times <!--\; ??\; -->{10}^3\mathrm{s}$ in typical CC supernova progenitors, and a corresponding spin period of $P_{\mathrm{m}\mathrm{a}\mathrm{x},\mathrm{N}\mathrm{S}}\lesssim <!--\; ???\; -->500\mathrm{m}\mathrm{s}$ for newborn neutron stars (NSs). This is comparable to the typical birth spin periods of most radio pulsars. Stochastic spin-up via IGWs during shell O/Si burning may thus determine the initial rotation rate of most NSs. For a given progenitor, this theory predicts a Maxwellian distribution in pre-collapse core rotation frequency that is uncorrelated with the spin of the overlying envelope.