Short answer. No. Islam holds every human life sacred, forbids harming non-combatants, and condemns terror. Terrorism breaks Islamic law — and mainstream Muslim scholars have said so, together and explicitly.
Where the idea comes from
A small number of violent groups commit atrocities while claiming to act for Islam, and those acts dominate the news. It is easy to mistake the loudest, ugliest minority for the faith of nearly two billion people.
Islam holds life sacred
One of the most quoted verses in the Quran equates the murder of a single innocent person with an attack on all of humanity:
"...whoever kills a soul unless for a soul or for corruption [done] in the land — it is as if he had slain mankind entirely. And whoever saves one — it is as if he had saved mankind entirely."
— Quran 5:32 (Saheeh International)1
Even toward enemies, the Quran commands justice rather than vengeance:
"...And do not let the hatred of a people prevent you from being just. Be just; that is nearer to righteousness."
— Quran 5:8 (Saheeh International)3
And the Prophet ﷺ placed the killing of a protected non-Muslim — anyone living under a covenant of safety — among the gravest of sins:
"Whoever killed a mu'ahid (a person granted the pledge of protection by the Muslims) shall not smell the fragrance of Paradise, though its fragrance can be smelt at a distance of forty years."
— Sahih al-Bukhari 31664
This is why scholars hold that deliberately targeting civilians — the very definition of terrorism — is forbidden in Islam, not licensed by it.876
Coexistence, not coercion
The Quran also frames the normal relationship with peaceful non-Muslims as one of kindness and fairness:
"Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes — from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly."
— Quran 60:8 (Saheeh International)2
Mainstream Muslim authorities have repudiated terrorism in the clearest collective terms — for example the Amman Message (2005), endorsed by hundreds of scholars across the Muslim world, which condemns the killing of innocents and the misuse of religion to justify it.5
In short
Islam does not promote terrorism; it forbids it. The Quran sanctifies human life, demands justice even toward enemies, and protects non-combatants — and the world's mainstream scholars have said so plainly. The violence of a few does not represent the teaching of the faith. See also What does jihad really mean?.