Hi Linda,
Welcome to Wikitree! I too am adopted, only fully. The template isn't obligatory but it is useful for people to see it. It might also help you to organise your family.
My recommendation is this:
Have your biological father listed as your father (for DNA purposes) but keep a profile for your adopted father linked through the adoption template on your profile page. That way, not only will it tell people the whole story in one easy view, it will also provide you with a nifty quick-link between families.
If you currently have your adopted father listed as your father you can go to your edit page and you will see an option in the right column to edit your parents. Just detach him and add your birth father's details. However, make sure you've made a note of his Wikitree ID for you to add to your template.
Hope this helps. Give me a shout if you need anything else and above all, enjoy the journey. :-)