Short answer
Yes. The Quran says again and again that Allah is over all things competent. Nothing possible is beyond His power, and He creates by saying "Be". Questions like "Can Allah create a rock He cannot lift?" ask about something self-contradictory, which is not a thing at all, so they say nothing against His power.
Sunni creed affirms qudrah (power) as an eternal attribute of Allah that extends to every possible thing. The Maturidi and Ash'ari scholars explain that power relates to what is possible, not to what is rationally impossible, such as Allah having a partner or ceasing to exist; this is His perfection, not a limit.
The four schools agree on this.
Explanation
"Indeed, Allah is over all things competent" appears many times in the Quran (for example 2:20). "His command is only when He intends a thing that He says to it, Be, and it is" (36:82). Among His names are al-Qadir (the Able) and al-Muqtadir (the All-Powerful). In the dua of istikhara the Prophet ﷺ taught us to say: You are able and I am not, You know and I do not.
So what about the puzzles? "Can Allah create a rock so heavy He cannot lift it?" or "Can Allah create another god?" Scholars of creed answered this long ago. Power is the ability to bring into being what is possible. A contradiction, like a square circle or a created being who is uncreated, is not a possible thing that power fails to reach; it is just words that cancel each other out. Saying Allah cannot do the impossible is like saying He cannot be weak: it describes His perfection.
A related question: can Allah do injustice? Allah says in a hadith qudsi: "O My servants, I have forbidden injustice for Myself." He does not do it, not from inability, but because injustice is a deficiency, and He is free of every deficiency.
Knowing this gives a believer calm. Nothing you face is too big for Him to change. Read about al-Qadir and al-Muqtadir, verses on trust in Allah and who created Allah?
The evidence
Quran, Surah Al-Baqara 2:20
يَكَادُ ٱلْبَرْقُ يَخْطَفُ أَبْصَٰرَهُمْ ۖ كُلَّمَآ أَضَآءَ لَهُم مَّشَوْا۟ فِيهِ وَإِذَآ أَظْلَمَ عَلَيْهِمْ قَامُوا۟ ۚ وَلَوْ شَآءَ ٱللَّهُ لَذَهَبَ بِسَمْعِهِمْ وَأَبْصَٰرِهِمْ ۚ إِنَّ ٱللَّهَ عَلَىٰ كُلِّ شَىْءٍۢ قَدِيرٌۭ ﴿٢٠﴾
The lightning almost snatches away their sight. Every time it lights [the way] for them, they walk therein; but when darkness comes over them, they stand [still]. And if Allah had willed, He could have taken away their hearing and their sight. Indeed, Allah is over all things competent.
Affirms Allah's power over everything.
Quran, Surah Yaseen 36:82
إِنَّمَآ أَمْرُهُۥٓ إِذَآ أَرَادَ شَيْـًٔا أَن يَقُولَ لَهُۥ كُن فَيَكُونُ ﴿٨٢﴾
His command is only when He intends a thing that He says to it, "Be," and it is.
Shows the ease of His creating.
Sahih al-Bukhari 1166
Sahih... فَإِنَّكَ تَقْدِرُ وَلاَ أَقْدِرُ وَتَعْلَمُ وَلاَ أَعْلَمُ وَأَنْتَ عَلاَّمُ الْغُيُوبِ ...
"For You are able and I am not, and You know and I do not, and You are the Knower of the unseen."
The Prophet ﷺ taught us to affirm Allah's power in dua.
Sahih Muslim 2577
Sahih... يَا عِبَادِي إِنِّي حَرَّمْتُ الظُّلْمَ عَلَى نَفْسِي ...
"O My servants, I have forbidden injustice for Myself."
Shows Allah does not do injustice because it is a deficiency.
Where the ruling is recorded
- al-Aqa'id al-Nasafiyya with Sharh al-Taftazani, Section on the attributes of Allah. Affirms power as an eternal attribute and explains that it relates to what is possible.
- al-Fiqh al-Akbar (Imam Abu Hanifa), Section on the attributes of essence. Lists power among Allah's eternal attributes.
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.