Short answer
Not as jewellery, since men may not wear bracelets. Wearing one purely as treatment is a medical question, and scholars warn that if a bracelet has no real proven effect and you believe it heals, it comes close to the amulets the Prophet ﷺ condemned. Use proven treatment and dua instead. A brace or band your doctor prescribes is a medical device and is fine.
Bracelets are women's adornment, and copper and brass are makruh tahrimi even for a man's ring. Treatment is permitted when its benefit is known by experience or medicine, but an object worn in the belief that it has hidden power to heal is forbidden.
The four schools agree on this.
Explanation
Copper and magnetic bracelets are sold to ease arthritis and joint pain. For a Muslim man there are two questions: whether he may wear a bracelet at all, and whether wearing one for health is lawful treatment or a kind of charm.
As jewellery. In the Hanafi school a man's only jewellery is a silver ring, and copper and brass are disliked even for rings. A copper or magnetic bracelet worn because it looks good is not allowed for men; see can Muslim men wear jewellery.
As treatment. The Prophet ﷺ told people to seek treatment, and the Hanafi scholars allow remedies whose benefit is known by experience or medicine. Medical research has generally not found a real effect from copper or magnetic bracelets. When something has no real link to the cure and people wear it believing it heals, it starts to look like the amulets the Prophet called shirk. A report that he told a man to remove a brass ring worn against weakness is often quoted here, but its chain is weak, so the ruling rests on the general principles instead.
What to do. Use treatment your doctor recommends, and ask Allah for healing; see dua for health. A compression sleeve, wrist brace or medical alert band is a medical item, not jewellery, and is fine. The caution about believing in a bracelet's healing power applies to women as well.
Ask a mufti about your own case. This answer explains the general ruling. When the details of your situation matter, as they do here, ask a qualified mufti and give them the full facts. Where to ask a scholar.
The evidence
Quran, Surah Ash-Shu'araa 26:80
وَإِذَا مَرِضْتُ فَهُوَ يَشْفِينِ ﴿٨٠﴾
And when I am ill, it is He who cures me
Healing comes from Allah, not from objects worn on the body.
Sunan Abi Dawud 3855
Graded sahih... تداووا فإن الله عز وجل لم يضع داء إلا وضع له دواء ...
"Seek treatment, for Allah has not created a disease without creating a cure for it."
Real treatment is encouraged.
Sunan Abi Dawud 3883
Graded sahih... إن الرقى والتمائم والتولة شرك ...
"Spells, amulets and love charms are shirk."
Objects worn in the belief that they have hidden power are condemned.
Where the ruling is recorded
- al-Hidaya, Kitab al-Karahiyya, section on clothing. Men's rings are of silver only; iron, brass and copper are disliked.
- al-Fatawa al-Hindiyya, Kitab al-Karahiyya, chapter on medical treatment. Treatment is permitted, and on amulets and charms.
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.