Partonic effects on collective flows at RHIC Higher-order anisotropic flows v_4 and v_6 of charged hadrons in heavy ion collisions at the Relativistic Heavy Ion Collider are studied in a multiphase transport. We find that the same parton scattering cross section of about 10 mb used in explaining the measured v_2 of charged hadrons can also reproduce the recent data on their v_4 and v_6 from Au + Au collisions at ¡Ìs=200 AGeV. It is further found that the v_4 is a more sensitive probe of the initial partonic dynamics in these collisions than v_2. Moreover, higher-order parton anisotropic flows are nonnegligible and satisfy the scaling relation v_{n,q} (p_{T})¡«v_{2,q}^{n/2}(p_{T}), which leads naturally to the observed similar scaling relation among hadron anisotropic flows when the coalescence model is used to describe hadron production from the partonic matter. In addition, the rapidity dependence of collective flows is also discussed.