No. Killing innocent people, Muslim or not, is one of the gravest sins in Islam. The Quran says whoever kills a soul unjustly, it is as if he had killed all of mankind.
The fuller answer
Terrorism, as the deliberate targeting of civilians to spread fear, has no basis in the Quran or the Sunnah. The Prophet ﷺ said, 'Whoever kills a person under a covenant of protection will not smell the fragrance of Paradise.' Suicide is forbidden, so 'suicide bombing' has no Islamic basis, and the scholars of all schools, from Al-Azhar to Saudi Arabia to Deoband, have condemned attacks such as 9/11 and many have issued fatwas against them.
Extremist groups cite verses out of context and have been rejected by the Muslim mainstream. The victims of terrorism are mostly Muslims. It is fair to ask why such groups exist in the Muslim world, and the answers include war, politics, poverty and misreadings of the religion, but the Islamic ruling is clear.
Because of that, We decreed upon the Children of Israel that 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. And our messengers had certainly come to them with clear proofs. Then indeed many of them, [even] after that, throughout the land, were transgressors.
And do not kill the soul which Allah has forbidden, except by right. And whoever is killed unjustly - We have given his heir authority, but let him not exceed limits in [the matter of] taking life. Indeed, he has been supported [by the law].
Say, "Come, I will recite what your Lord has prohibited to you. [He commands] that you not associate anything with Him, and to parents, good treatment, and do not kill your children out of poverty; We will provide for you and them. And do not approach immoralities - what is apparent of them and what is concealed. And do not kill the soul which Allah has forbidden [to be killed] except by [legal] right. This has He instructed you that you may use reason."
O you who have believed, do not consume one another's wealth unjustly but only [in lawful] business by mutual consent. And do not kill yourselves [or one another]. Indeed, Allah is to you ever Merciful.
Sources
The hadith and reports behind this answer. Open a number to read it on sunnah.com.
This answer follows the mainstream Sunni understanding and is general learning, not a fatwa. Where Muslims differ, the answer says so. Have a question of your own? Write to us.