Is there anything I can do to encourage my brother to forgive me?
Did you apologize? Did you show him that you are aware of your error and have taken steps not to repeat it? This may help him establish trust in you which may help him to forgive you. You will need patience as he makes up his own mind. Your trying to put pressure on him to forgive will not be helpful. He needs to see the value of forgiveness and willingly say yes to it.
For additional information, see Learning to Forgive Others.