There is nothing in the Catechism of the Church or in her history that suggests that any theologian held this belief. The passage mostly quoted by people is St Pauls:
Or do you not know that the Lord’s people will judge the world? And if you are to judge the world, are you not competent to judge trivial cases? Do you not know that we will judge angels? How much more the things of this life! 1 Cor 6:2-3
However, this doesn’t make any sense when considered literally. Some theologians believe that what St Paul was referring to was that man will judge the fallen Angels and not the Angels in heaven who, as we know, have no sin. So if they have no sin, what’s the point of judging them?.
Before the fall of Angels, they were “tested”, and most of them fell. Many of those fallen angels are still at work in our world, they are the demons who tempt the people of God. So, maybe, they will be judged by the very same faithfuls they tornmented.
Help from Angels are usually seen as God’s work, these beings had the power to make judgements and pronouce punishments on stubborn people while on God’s mission. Their actions are somewhat divine since they act in God’s stead:
But when we cried out to the LORD, He heard our voice and sent an angel and brought us out from Egypt; now behold, we are at Kadesh, a town on the edge of your territory. – Numbers 20:16
Then Nebuchadnezzar said, “Praise be to the God of Shadrach, Meshach and Abednego, who has sent his angel and rescued his servants! They trusted in him and defied the king’s command and were willing to give up their lives rather than serve or worship any god except their own God. Daniel 3:28
Then Peter came to himself and said, “Now I know without a doubt that the Lord has sent his angel and rescued me from Herod’s clutches and from everything the Jewish people were hoping would happen.” – Acts 12:11
Human beings are of a “lower rank” than them:
what is mankind that you are mindful of them,
human beings that you care for them?
You have made them a little lower than the angels
and crowned them with glory and honor – Psalm 8:4-5