Swift heavy ions induce a high density of electronic excitations that can cause the formation of amorphous ion tracks in insulators. No ion tracks have been observed in the semiconductor SiC, but recent experimental work suggests that irradiation damaged SiC can undergo defect recovery under swift heavy ion irradiation. It is believed that local heating of the lattice due to the electronic energy deposition can anneal, and thereby recover, some of the disordered structure. We simulate the local heating due to the ions by the inelastic thermal spike model and perform molecular dynamics simulations of different model damage states to study the defect recovery on an atomistic level. We find significant recovery of point defects and a disordered layer, as well as recrystallization at the amorphous-to-crystalline interface of an amorphous layer. The simulation results support the swift heavy ion annealing hypothesis.