The controlled creation of defects in silicon carbide represents a major challenge. A well-known and efficient tool for defect creation in dielectric materials is the irradiation with swift (E(kin) ≥ 500 keV/amu) heavy ions, which deposit a significant amount of their kinetic energy into the electronic system. However, in the case of silicon carbide, a significant defect creation by individual ions could hitherto not be achieved. Here we present experimental evidence that silicon carbide surfaces can be modified by individual swift heavy ions with an energy well below the proposed threshold if the irradiation takes place under oblique angles. Depending on the angle of incidence, these grooves can span several hundreds of nanometres. We show that our experimental data are fully compatible with the assumption that each ion induces the sublimation of silicon atoms along its trajectory, resulting in narrow graphitic grooves in the silicon carbide matrix.