Yes, it is permissible to give zakaah to someone who wants to get married, if he does not have enough money to get married. This is included in the eight categories mentioned in the verse in which Allaah says (interpretation of the meaning):
“As-Sadaqaat (here it means Zakaah) are only for the Fuqaraa’ (poor), and Al-Masaakeen (the poor) and those employed to collect (the funds); and to attract the hearts of those who have been inclined (towards Islam); and to free the captives; and for those in debt; and for Allaah’s Cause (i.e. for Mujaahidoon — those fighting in a holy battle), and for the wayfarer (a traveller who is cut off from everything); a duty imposed by Allaah. And Allaah is All-Knower, All-Wise”
The one who does not have enough money is poor, so it is permissible to give him zakaah.
Shaykh Ibn ‘Uthaymeen said: If we find a person who can earn enough for food and drink and accommodation, but he needs to get married and does not have enough to do so, is it permissible for us to get him married using zakaah funds? The answer is: yes, it is permissible to get him married using zakaah funds, and to give him the mahr in full.
If it is said: how come it is permissible to get a poor man married using zakaah funds even if what is given to him is a large amount? We say: because a man’s need to get married is urgent, and in some cases it may be like his need for food and drink. Hence the scholars said that the one who is obliged to spend on a person must marry him off if he can afford that. So the father must marry his son off if the son needs to get married but does not have the means of doing so. But I heard that some fathers forget how they were when they were young, and when their sons ask them to help them get married, they say: “Pay for marriage from your own pocket.” This is not permissible, and it is haraam if he is able to get him married. His son will confront him on the Day of Resurrection if he does not get him married when he is able to.
Fataawa Arkaan al-Islam, p. 440-441.
Shaykh Ibn Baaz (may Allaah have mercy on him) was asked about giving zakaah to a young man who cannot afford to get married. He said:
It is permissible to give zakaah to this young man, to help him get married, if he cannot afford it.
Fataawa al-Shaykh Ibn Baaz, 14/275.
The Standing Committee was asked:
Is it permissible to give zakaah to a young man who wants to get married in order to guard his chastity?
That is permissible if he cannot afford the customary expenses of marriage where there is no extravagance.
Fataawa al-Lajnah al-Daa’imah, 10/17.
And Allaah knows best.