Of course you can! But is it a good idea? If one day you can get on the International Space Station, for example, or just go into orbit around the Earth and fall into weightlessness, you will probably want to shed at least one tear of emotion. You’d better not! Why?
Canadian astronaut Chris Hadfield shows why. True, his “tear” is a bit more generous than usual, but, as you can see, the tears are not willing to leave you in space. They stay with you. They do not really want to go! At least until you find enough dry towel. Look.