God absolutely appointed Hitler to serve God's purpose. He has appointed everyone that has or has held a position of authority. God also appointed all of the kings, as mentioned in the Old Testament, even though most did evil in the eyes of the Lord.
God has orchestrated all events in the past, the events today, and the events to come. There is prophesy that had to be fulfilled, in the past, now, and in the future. God leaves nothing to chance and is complete control of all final outcomes.
I do not believe for one second God is accountable or the author of evil.
A better translation is: (Romans 13:1) 13 Let every person be in subjection to the superior authorities, for there is no authority except by God; the existing authorities stand placed in their relative positions by God.