An electron current can move atoms in a nanoscale device with important consequences for the device operation and breakdown. We perform first principles calculations aimed at evaluating the possibility of changing the energy barriers for atom migration in carbon-based systems. In particular, we consider the migration of adatoms and defects in graphene and carbon nanotubes. Although the current-induced forces are large for both the systems, in graphene the force component along the migration path is small and therefore the barrier height is little affected by the current flow. In contrast, the same barrier is significantly reduced in carbon nanotubes as the current increases. Our work also provides a real-system numerical demonstration that current-induced forces within density functional theory are non-conservative. © 2016 The Royal Society of Chemistry.