Things have not gone well for King Lear earlier in the play. His family life is in disarray, he's living with his mouthy and greedy eldest daughter. By the time in Scene 4 when King Lear utters the line you are asking about, he has mocked by his fool, sassed by Oswald, and his daughter has been very disrespectful in talking back to him. Aside from her attitude, she goes even further in telling him about the misbehavior of those who should be responsible members of his court.
The king can't believe the way in which he is being treated by all who are around him. His question, "Who is it that can tell me who I am?" is his seeking of someone who will affirm his rightful authority and position as the king.