Red giant (RGB) stars in the field and in globular clusters present abundance anomalies that can not be explained by standard stellar evolution models. Some of these peculiarities, in particular those concerning lithium, carbon and nitrogen for stars more luminous than the bump, attest the presence of extra-mixing processes at play inside the stars. Although their nature remains unclear, rotation has often been invoked as a possible source for mixing inside RGB stars (Sweigart & Mengel 1979; Charbonnel 1995; Denissenkov & Tout 2000). Much work has been done during the last decade on the description of rotation-induced mixing and on the transport of angular momentum and chemicals by meridional circulation and shear turbulence (Zahn 1992, etc.). Within this framework, we present the first fully consistent computations of rotating low mass and low metallicity stars from the Zero Age Main Sequence (ZAMS) to the upper RGB. When self-consistent evolution of the internal distribution of angular momentum is taken into account, it is found that meridional circulation and shear instability by themselves are not able to produce the required amount of mixing to account for the observed abundance patterns.