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The core rotation rates of massive stars have a substantial impact on the nature of core collapse supernovae and their compact remnants. We demonstrate that internal gravity waves (IGW), 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 ($10 M_\odot \lesssim M \lesssim 20 M_\odot$) supernova progenitors, IGW may substantially spin down the core, leading to iron core rotation periods $(P_{\rm Fe} min,Fe}  \gtrsim 50 \, {\rm s})$. Angular momentum (AM) conservation during the supernova would entail minimum NS rotation periods of $P_{\rm NS} min,NS}  \gtrsim 3 \, {\rm ms}$. In most cases, the combined effects of magnetic torques and IGW AM transport likely lead to substantially slower longer  rotation periods. Stochastic influxes of AM carried by IGW during shell burning phases also entail a maximum core rotation period. We estimate $P_{\rm Fe} max,Fe}  \lesssim 10^4 \, {\rm s}$ in most core collapse supernova progenitors, and a corresponding spin period of $P_{\rm max,  NS} \lesssim 400 \, {\rm ms}$ for the newborn neutron star. Therefore, in the event of efficient core spin-down via waves/magnetic torques in previous stages of evolution, stochastic spin-up via IGW during shell O/Si burning may primarily determine the initial rotation rate of ordinary pulsars.