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Abstract Cosmic rays (CRs) are the primary driver of ionization in star-forming molecular clouds (MCs). Despite their potential impacts on gas dynamics and chemistry, no simulations of star cluster formation following the creation of individual stars have included explicit cosmic-ray transport (CRT) to date. We conduct the first numerical simulations following the collapse of a 2000M_⊙MC and the subsequent star formation including CRT using the STAR FORmation in Gaseous Environments framework implemented in the GIZMO code. We show that when CRT is streaming-dominated, the CR energy in the cloud is strongly attenuated due to energy losses from the streaming instability. Consequently, in a Milky Way–like environment the median CR ionization rate in the cloud is low (ζ≲ 2 × 10⁻¹⁹s⁻¹) during the main star-forming epoch of the calculation and the impact of CRs on the star formation in the cloud is limited. However, in high-CR environments, the CR distribution in the cloud is elevated (ζ≲ 6 × 10⁻¹⁸), and the relatively higher CR pressure outside the cloud causes slightly earlier cloud collapse and increases the star formation efficiency by 50% to ∼13%. The initial mass function is similar in all cases except with possible variations in a high-CR environment. Further studies are needed to explain the range of ionization rates observed in MCs and explore star formation in extreme CR environments.