Short answer
Not in the sense of judging souls. Muslims believe Allah alone judges every person on the Day of Judgement. The Prophet ﷺ said Jesus will return before the end as a just ruler (hakam) on earth, governing by the law of Islam. On the Last Day, the Quran says, Jesus will be a witness over the People of the Book.
The descent of Isa near the end of time is part of Sunni creed. His role then is to rule justly by the shariah of Muhammad ﷺ, not to bring a new law. Judgement and reckoning on the Day of Resurrection belong to Allah alone.
The four schools agree on this.
Explanation
In Islam, the Day of Judgement belongs to Allah. Muslims repeat in every unit of prayer that He is the Sovereign of the Day of Recompense. No prophet, angel or saint shares in that.
The idea of Jesus judging comes, for Muslims, from the hadith about his return. The Prophet ﷺ swore that the son of Mary will soon descend among the Muslims as a hakam muqsit, a just judge or ruler, who will break the cross, kill the swine and end the jizya. Scholars explain this as ruling and settling disputes on earth: he will end the arguments about himself and lead by the shariah of Islam. See will Jesus return.
On the Day of Resurrection, Jesus appears as a witness and a servant, not as the judge. The Quran says he will be a witness against the People of the Book, and that Allah will ask him whether he told people to worship him and his mother. He will answer: it was not for me to say what I had no right to say.
In the long hadith of intercession, people go from prophet to prophet asking for help on that Day. When they reach Jesus, he sends them on to Muhammad ﷺ. So Muslims honour Jesus as a mighty prophet who will return, while holding that judgement is Allah's alone. See what happened to Jesus.
The evidence
Quran, Surah Al-Faatiha 1:4
مَٰلِكِ يَوْمِ ٱلدِّينِ ﴿٤﴾
Sovereign of the Day of Recompense.
Allah alone is the judge on the Last Day.
Quran, Surah An-Nisaa 4:159
وَإِن مِّنْ أَهْلِ ٱلْكِتَٰبِ إِلَّا لَيُؤْمِنَنَّ بِهِۦ قَبْلَ مَوْتِهِۦ ۖ وَيَوْمَ ٱلْقِيَٰمَةِ يَكُونُ عَلَيْهِمْ شَهِيدًۭا ﴿١٥٩﴾
And there is none from the People of the Scripture but that he will surely believe in Jesus before his death. And on the Day of Resurrection he will be against them a witness.
Jesus is a witness on that Day, not the judge.
Quran, Surah Al-Maaida 5:116
وَإِذْ قَالَ ٱللَّهُ يَٰعِيسَى ٱبْنَ مَرْيَمَ ءَأَنتَ قُلْتَ لِلنَّاسِ ٱتَّخِذُونِى وَأُمِّىَ إِلَٰهَيْنِ مِن دُونِ ٱللَّهِ ۖ قَالَ سُبْحَٰنَكَ مَا يَكُونُ لِىٓ أَنْ أَقُولَ مَا لَيْسَ لِى بِحَقٍّ ۚ إِن كُنتُ قُلْتُهُۥ فَقَدْ عَلِمْتَهُۥ ۚ تَعْلَمُ مَا فِى نَفْسِى وَلَآ أَعْلَمُ مَا فِى نَفْسِكَ ۚ إِنَّكَ أَنتَ عَلَّٰمُ ٱلْغُيُوبِ ﴿١١٦﴾
And [beware the Day] when Allah will say, "O Jesus, Son of Mary, did you say to the people, 'Take me and my mother as deities besides Allah?'" He will say, "Exalted are You! It was not for me to say that to which I have no right. If I had said it, You would have known it. You know what is within myself, and I do not know what is within Yourself. Indeed, it is You who is Knower of the unseen.
Jesus himself will be questioned by Allah.
Sahih al-Bukhari 2222
Sahih... ليوشكن أن ينزل فيكم ابن مريم حكما مقسطا ...
"The son of Mary will soon descend among you as a just judge."
His role on his return is to rule justly on earth.
Sahih al-Bukhari 4712
Sahih... اذهبوا إلى غيري اذهبوا إلى محمد ...
"Go to someone else; go to Muhammad."
Jesus will direct people to Muhammad ﷺ for intercession on the Day of Judgement.
Where the ruling is recorded
- al-Fiqh al-Akbar, the section on the signs of the Hour. Lists the descent of Isa among the true signs of the Hour.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.