We assessed cerebral asymmetry for language in 35 monozygotic twin pairs. Using DTI, we reconstructed the arcuate fasciculus in each twin. Among the male twins, right-handed pairs showed greater left-sided asymmetry of connectivity in the arcuate fasciculus than did those with discordant handedness, and within the discordant group the right-handers had greater left-sided volume asymmetry of the arcuate fasciculus than did their left-handed co-twins. There were no such effects in the female twins. Cerebral asymmetry for language showed more consistent results, with the more left-cerebrally dominant twins also showing more leftward asymmetry of high anisotropic fibers in the arcuate fasciculus, a result applying equally to female as to male twins. Reversals of arcuate fasciculus asymmetry were restricted to pairs discordant for language dominance, with the left-cerebrally dominant twins showing leftward and the right-cerebrally dominant twins rightward asymmetry of anisotropic diffusion in the arcuate fasciculus. Because monozygotic twin pairs share the same genotype, our results indicate a strong nongenetic component in arcuate fasciculus asymmetry, particularly in those discordant for cerebral asymmetry.