Dale is correct, my brother is my half-brother. I know who his father was and added him as the father of my brother. Then I put the fact that he was adopted by my father on my father's profile and linked it back to my brother. I also noted the fact on my Brother's profile.
However, Wikitree now lets you indicate that a parent is non-biological. So, you could leave the adopting father in place and use the indicator that he is non-biological. This removes him from any DNA calculations.
When you add siblings, look for a check box at the bottom of the add page and you should be able to uncheck the Other Parent as it is checked by default.