We have investigated the formation of cross-links between neighboring carbon nanotubes within a bundle. Classical molecular dynamics was used to follow the evolution of the system when it is bombarded by low-energy carbon atoms. We show that it is possible to polymerize carbon nanotubes through irradiation and discuss the most common types of defects produced. Cross-links are created mainly in the direction perpendicular to the surface, and for higher energies, defects are created deeper in the rope. The final defects geometries may provide a realistic input to electronic density first principle calculations.