Short answer
Yes, as a species. Kangaroo eats plants and is not a predator, so it is among the good animals Muslims may eat, and the schools do not differ on it. But it must be slaughtered the Islamic way; most kangaroo meat in shops comes from wild animals shot by commercial hunters, which is not halal.
Kangaroo is halal (mubah) when slaughtered with tasmiyah, since it is a plant eater and not among the predators, vermin or repulsive animals the school forbids. In the Hanafi school an animal killed by a bullet is halal only if it is reached alive and then slaughtered.
The four schools agree on this.
Explanation
No classical book mentions the kangaroo, so scholars apply the general rules. A land animal is halal unless it is a pig, a predator that hunts with its fangs, a bird of prey, a domestic donkey or mule, or one of the creeping and repulsive creatures. The kangaroo is none of these: it is a grazing animal, like a deer. Contemporary scholars of the four schools therefore treat it as halal.
The species is only half the question. Like any land animal, kangaroo must be slaughtered by cutting the throat with Allah's name. Almost all commercial kangaroo meat in Australia comes from wild animals shot in the field by licensed shooters. That is not zabiha, so supermarket kangaroo, kangaroo pet food and most restaurant kangaroo are not halal unless a halal certifier confirms the method.
Hunting it yourself raises a Hanafi point. Game is lawful when a sharp weapon wounds it and Allah's name is said. A bullet kills mainly by force, and the Hanafi school compares it to the blunt side of an arrow, which the Prophet ﷺ said makes the game unlawful. So a Hanafi hunter must reach the animal while it is still alive and slaughter it. Some scholars of other schools accept a bullet with bismillah.
See also what makes meat halal and which animals are haram.
The evidence
Quran, Surah Al-Maaida 5:4
يَسْـَٔلُونَكَ مَاذَآ أُحِلَّ لَهُمْ ۖ قُلْ أُحِلَّ لَكُمُ ٱلطَّيِّبَٰتُ ۙ وَمَا عَلَّمْتُم مِّنَ ٱلْجَوَارِحِ مُكَلِّبِينَ تُعَلِّمُونَهُنَّ مِمَّا عَلَّمَكُمُ ٱللَّهُ ۖ فَكُلُوا۟ مِمَّآ أَمْسَكْنَ عَلَيْكُمْ وَٱذْكُرُوا۟ ٱسْمَ ٱللَّهِ عَلَيْهِ ۖ وَٱتَّقُوا۟ ٱللَّهَ ۚ إِنَّ ٱللَّهَ سَرِيعُ ٱلْحِسَابِ ﴿٤﴾
They ask you, [O Muhammad], what has been made lawful for them. Say, "Lawful for you are [all] good foods and [game caught by] what you have trained of hunting animals which you train as Allah has taught you. So eat of what they catch for you, and mention the name of Allah upon it, and fear Allah." Indeed, Allah is swift in account.
Good, wholesome animals are lawful by default.
Sahih al-Bukhari 5503
Sahih... ما أنهر الدم وذكر اسم الله فكل ...
"Whatever makes the blood flow and has Allah's name mentioned over it, eat it."
A halal species still needs a proper cut with Allah's name.
Sahih al-Bukhari 5475
Sahih... وما أصاب بعرضه فهو وقيذ ...
"What it strikes with its edge, eat; what it strikes with its broad side has been killed by a blow (waqidh)."
The Hanafi basis for not eating game killed by blunt force, applied to bullets.
Where the ruling is recorded
- al-Hidaya, Kitab al-Dhaba'ih, on what may be eaten. Land animals are lawful unless they fall into a forbidden category.
- Bada'i al-Sana'i, Kitab al-Dhaba'ih wa al-Suyud. Game must be wounded by a sharp edge; game killed by impact is not lawful.
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.