Praise be to Allah.
It is not permissible, because it is not permissible for men to use silk as clothing or for any other purpose. It is permissible for women to wear it. This usage of silk is a men’s affair, hence it is haraam. We should not be deceived by the fact that so many people follow this custom, or that so many people see it and do not speak out against it. This is like all other haraam things that people customarily do. A group of our companions have clearly stated that it is haraam to write the dowry on silk. And Allaah knows best.