Numerical models of molecular cloud cores are obtained, with assumed Gaussian random velocity fields that are consistent with moderate turbulence. If the velocity power spectrum is taken to be P(k) ∼ kn, with n = − 4 or −3, then the constructed line-of-sight velocity maps on the plane of the sky show gradients that can be interpreted as rotation. Deduced values of angular velocity, angular momentum, and dimensionless rotational parameter β are consistent with observations. The velocity gradient Ω, of an individual core is not a good indicator of its intrinsic angular momentum J/M. However, the distribution of deduced angular momenta from a large sample of cores with different random velocity fields is close to the distribution of actual angular momenta of these model cores if one assumes J/M = pΩR2 where R is the core radius and p must be determined from a Monte-Carlo study. For centrally condensed cores the standard value of p = 0.4 overestimates the mean intrinsic angular momentum by a factor of 3.