Short answer: No. In the Islamic religion, the rule is reserved only for Allah, and it is not allowed to provide legislative rights to any human being.
The Scripture of Muslims (Qur’an):
Quran 12:40–You worship not besides Him except [mere] names you have named them, you and your fathers, for which Allah has sent down no authority. Legislation is not but for Allah . He has commanded that you worship not except Him. That is the correct religion, but most of the people do not know.
Quran 6:57–Say, “Indeed, I am on clear evidence from my Lord, and you have denied it. I do not have that for which you are impatient. The decision is only for Allah . He relates the truth, and He is the best of deciders.”
Quran 40:12–[They will be told], “That is because, when Allah was called upon alone, you disbelieved; but if others were associated with Him, you believed. So the judgement is with Allah , the Most High, the Grand.”
Quran 95:8–Is not Allah the most just of judges?
Quran 5:50–Then is it the judgement of [the time of] ignorance they desire? But who is better than Allah in judgement for a people who are certain [in faith].
Quran 33:36–It is not for a believing man or a believing woman, when Allah and His Messenger have decided a matter, that they should [thereafter] have any choice about their affair. And whoever disobeys Allah and His Messenger has certainly strayed into clear error.
Quran 18:26–Say, ” Allah is most knowing of how long they remained. He has [knowledge of] the unseen [aspects] of the heavens and the earth. How Seeing is He and how Hearing! They have not besides Him any protector, and He shares not His legislation with anyone.”
Quran 5:44–And whoever does not judge by what Allah has revealed – then it is those who are the disbelievers.
The Traditions of Muhammad (Hadith):
Sahih Muslim 1731–When you meet your enemies who are polytheists [Christians…], invite them to three courses of action. If they respond to any one of these, you also accept it and withhold yourself from doing them any harm. Invite them to (accept) Islam; if they respond to you, accept it from them and desist from fighting against them … If they refuse to accept Islam, demand from them the Jizya. If they agree to pay, accept it from them and hold off your hands. If they refuse to pay the tax, seek Allah’s help and fight them.
Sahih al-Bukhari 7137–Narrated Abu Huraira: Allah’s Messenger (ﷺ) said, “Whoever obeys me, obeys Allah, and whoever disobeys me, disobeys Allah, and whoever obeys the ruler I appoint, obeys me, and whoever disobeys him, disobeys me.”
Islamic Scholarship (including Fatwas):
Tariq Ramadan(Speaking at the Islamic Center in Bielefeld, Germany on May 21, 2008) –My brothers and sisters, we must exploit the so-called democracy and freedom of speech here in the West to reach our goals. Our prophet Mohammed, peace be upon him and the Koran teach us that we must use ever conceivable means and opportunity to defeat the enemies of Allah. Tell the infidels in public; we respect your laws and your constitutions, which we Muslims believe that these are as worthless as the paper they are written on. The only law we must respect and apply is the Sharia.
Mawsoo’at al-Adyaan wa’l-Madhaahib al-Mu’aasirah (2/1066, 1067)— Undoubtedly the democratic system is one of the modern forms of shirk, in terms of obedience and following, or legislation, as it denies the sovereignty of the Creator and His absolute right to issue laws, and ascribes that right to human beings.
Fataawa al-Lajnah al-Daa’imah (23/406, 407)–It is not permissible for a Muslim to nominate himself in the hope that he can become part of a system which rules according to something other than that which Allaah has revealed and operates according to something other than the sharee’ah of Islam. It is not permissible for a Muslim to vote for him or for anyone else who will work in that government, unless the one who nominates himself or those who vote for him hope that by getting involved in that they will be able to change the system to one that operates according to the sharee’ah of Islam, and they are using this as a means to overcome the system of government, provided that the one who nominates himself will not accept any position after being elected except one that does not go against Islamic sharee’ah.
Fataawa al-Lajnah al-Daa’imah (1/373)–The Muslims in a country that is not governed according to Islamic sharee’ah should do their utmost and strive as much as they can to bring about rule according to Islamic sharee’ah, and they should unite in helping the party which is known will rule in accordance with Islamic sharee’ah. As for supporting one who calls for non-implementation of Islamic sharee’ah, that is not permissible, rather it may lead a person to kufr
Shaykh Muhammad Saalih al-Munajjid (Fatwa no 107166)–Democracy is a man-made system, meaning rule by the people for the people. Thus it is contrary to Islam, because rule is for Allaah, the Most High, the Almighty, and it is not permissible to give legislative rights to any human being, no matter who he is… The one who understands the true nature of the democratic system and the ruling thereon, then he nominates himself or someone else (for election) is approving of this system, and is working with it, is in grave danger, because the democratic system is contrary to Islam and approving of it and participating in it are actions that imply apostasy and being beyond the pale of Islam.
A Former Muslim Notes:
In Islam, democracy is considered a man-made system. It is a system which encourages the rule of people. In the Islamic religion, the rule is reserved only for Allah, and it is not allowed to provide legislative rights to any human being.Therefore, by nature, it is contrary to Islam.
Moreover, democracy is considered a new form of heretical idolatry. As one scholar puts it, ‘undoubtedly the democratic system is one of the modern forms of shirk [idolatory], in terms of obedience and following, or legislation, as it denies the sovereignty of the Creator and His absolute right to issue law, and ascribes that right to human beings.’
According to Muslim scholars, those who fully understand the nature of democracy but still choose to nominate themselves are considered apostates. Why? Because Islam and democracy are two different systems that cannot coexist and those who subscribe to the democratic system are actually rejecting Islamic system.
But an exemption is made for those Muslims who are getting involved in the democratic system so that they can one day change the system from democracy to Sharia. One scholar puts it, ‘unless the one who nominates himself or those who vote for him hope that by getting involved in that they will be able to change the system to one that operates according to the Shari’a of Islam, and they are using this as a means to overcome the system of government.’
Islam permits no other law except for the law of Sharia, In the words of Shaykh Muhammad Saalih al-Munajjid, ‘It is not permissible for anyone to follow a system or methodology other than Islam. One of the indications of their acceptance of Allah as their Lord, Islam as their religion, and Muhammad (blessings and peace of Allah be upon him) as their Prophet and Messenger, is that the Muslims adhere to Islam outwardly and inwardly; they respect the laws of Allah and follow the Sunnah of the Prophet (blessings and peace of Allah be upon him).’
We can conclude . Therefore, Islam and democracy cannot coexist.