In the mature human brain, the arcuate fasciculus mediates verbal working memory, word learning, and sublexical speech repetition. However, its contribution to early language acquisition remains unclear. In this work, we aimed to evaluate the role of the direct segments of the arcuate fasciculi in the early acquisition of linguistic function. We imaged a cohort of 43 preterm born infants (median age at birth of 30 gestational weeks; median age at scan of 42 postmenstrual weeks) using high b value high-angular resolution diffusion-weighted neuroimaging and assessed their linguistic performance at 2 years of age. Using constrained spherical deconvolution tractography, we virtually dissected the arcuate fasciculi and measured fractional anisotropy (FA) as a metric of white matter development. We found that term equivalent FA of the left and right arcuate fasciculi was significantly associated with individual differences in linguistic and cognitive abilities in early childhood, independent of the degree of prematurity. These findings suggest that differences in arcuate fasciculi microstructure at the time of normal birth have a significant impact on language development and modulate the first stages of language learning.