Short answer
Yes. A man's arms are not part of his awrah, so short-sleeved shirts and T-shirts are fine, and a prayer in them is valid. The Hanafi scholars dislike rolling up long sleeves for prayer, and praying in clothes you would not wear to meet respectable people.
Short sleeves are mubah for men. Praying with long sleeves rolled or tucked up (kaff al-thawb) is makruh, and many muftis say makruh tahrimi. Praying in a short-sleeved shirt is valid, though it is better to pray in your fuller, better clothes when you can.
The four schools agree on this.
Explanation
A man's awrah is from the navel to the knees; see the awrah guide. The arms are outside it, and the four schools agree on this. So wearing a T-shirt or short-sleeved shirt in daily life is permitted.
In prayer. The Prophet ﷺ said he was commanded to prostrate on seven bones and not to tuck up his hair or his clothes. The Hanafi scholars take from this that rolling up sleeves or a hem for prayer is disliked. This catches many people after wudu: if your sleeves are long, roll them down before you start.
A shirt made with short sleeves is not the same as rolling up long ones, so your prayer in it is fine. Still, Allah tells us to take our adornment at every masjid, and the Hanafi texts dislike praying in work or casual clothes you would not wear before respectable people. For Jumuah and when you go to the mosque, a fuller outfit is better; see what to wear to the mosque.
- Short-sleeved shirt: fine, in and out of prayer.
- Long sleeves rolled up to the elbow in prayer: disliked; roll them down.
- Sleeveless vests and tank tops: see can Muslim men go shirtless.
The evidence
Quran, Surah Al-A'raaf 7:31
۞ يَٰبَنِىٓ ءَادَمَ خُذُوا۟ زِينَتَكُمْ عِندَ كُلِّ مَسْجِدٍۢ وَكُلُوا۟ وَٱشْرَبُوا۟ وَلَا تُسْرِفُوٓا۟ ۚ إِنَّهُۥ لَا يُحِبُّ ٱلْمُسْرِفِينَ ﴿٣١﴾
O children of Adam, take your adornment at every masjid, and eat and drink, but be not excessive. Indeed, He likes not those who commit excess.
Believers are told to dress well for the mosque and prayer, without excess.
Sahih al-Bukhari 816
Sahih... أمرت أن أسجد على سبعة لا أكف شعرا ولا ثوبا ...
"I was commanded to prostrate on seven bones and not to tuck up hair or clothes."
The basis for disliking rolled-up sleeves in prayer.
Where the ruling is recorded
- al-Durr al-Mukhtar with Radd al-Muhtar, Kitab al-Salah, chapter on what is disliked in prayer. Rolling up the sleeve or tucking up the clothes in prayer is disliked.
- Nur al-Idah with Maraqi al-Falah, Chapter on the disliked acts of prayer. Praying in work clothes and with rolled sleeves.
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.