Can an employee take promotional items from the company for his own use?

If the company where you work gives you these things to keep, then there is nothing wrong with taking them and using them, so long as they are permissible according to Islamic rulings. But if the company gives them to you to distribute to people outside the company for advertising and promotional purposes, then you have no right to take them unless you have been given permission to do so. And Allaah knows best.