how to create a "Fahrradstraße"?

In Germany, there are “Fahrradstraßen” i.e. with a bicycle you can use these streets in both directions instead of car users, who can use them only in one direction. Is there a function in the OSM-Editors to mark them?

Since you ask for Germany I take it that you speak German. Have a look at: on how to tag those roads. You might have to add those tags described there manually. How to do that depends on the editor you are using.