  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 $2000
M_{\odot}$ MC and the subsequent star formation including CRT using the
STARFORGE framework implemented in the GIZMO code. We show that when
CR-transport 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 (CRIR) in the
cloud is low ($ \zeta \lesssim 2 \times 10^{-19} \rm s^{-1}$) during the main
star forming epoch of the calculation and the impact of CRs on the star
formation in the cloud is limited. However, in high-CR environments, the CR
distribution in the cloud is elevated ($\zeta \lesssim 6 \times 10^{-18}$), and
the relatively higher CR pressure outside the cloud causes slightly earlier
cloud collapse and increases the star formation efficiency (SFE) by $50 \%$ to
$\sim 13 \%$. The initial mass function (IMF) 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.
