I Made two drafts of this answer depending on how much detail is required, please choose the appropriate one and let me know if edits are required.
DRAFT ONE:
No, you don't have to convert to marry a Muslim man. It is permissible for a Muslim man to marry a non-Muslim woman if she is Christian or Jewish, but it is not permissible for him to marry a non-Muslim woman who follows any religion other than these two and she must convert to be able to marry him.
The evidence for this is found in the Quran as:
Made lawful to you this day are At‑Tayyibaat [all kinds of Halaal (lawful) foods, which Allaah has made lawful. The food (slaughtered cattle, eatable animals) of the people of the Scripture (Jews and Christians) is lawful to you and yours is lawful to them. (Lawful to you in marriage) are chaste women from the believers and chaste women from those who were given the Scripture (Jews and Christians) before your time when you have given their due Mahr (bridal-money given by the husband to his wife at the time of marriage), desiring chastity (i.e. taking them in legal wedlock) not committing illegal sexual intercourse, nor taking them as (secret) lovers. -- Al-Maa'idah (5:4)
It is important to note here, that if a non-Muslim woman were to marry a Muslim man, he can only so much as invite her to Islam and teach her about his religion. But he cannot force her to convert by placing embracing Islam a condition for marriage or otherwise as God says in the Quran: "Let there be no compulsion in religion...." (Al Baqarah 2:256)
Therefore in light of the aforementioned verse, if you are a Christian or a Jewish woman, you do not need to convert to Islam to marry a muslim man.
DRAFT TWO:
No, you don't have to convert to marry a Muslim man. It is permissible for a Muslim man to marry a non-Muslim woman if she is Christian or Jewish, but it is not permissible for him to marry a non-Muslim woman who follows any religion other than these two and she must convert to be able to marry him.
It is important to note here, that if a non-Muslim woman were to marry a Muslim man, he can only so much as invite her to Islam and teach her about his religion. But he cannot force her to convert by placing embracing Islam a condition for marriage or otherwise as God says in the Quran: "Let there be no compulsion in religion...." (Al Baqarah 2:256)
Read On:
The evidence for Muslim men being allowed to marry women who are Christian and Jews can be found in the Quran as:
Made lawful to you this day are At‑Tayyibaat [all kinds of Halaal (lawful) foods, which Allaah has made lawful. The food (slaughtered cattle, eatable animals) of the people of the Scripture (Jews and Christians) is lawful to you and yours is lawful to them. (Lawful to you in marriage) are chaste women from the believers and chaste women from those who were given the Scripture (Jews and Christians) before your time when you have given their due Mahr (bridal-money given by the husband to his wife at the time of marriage), desiring chastity (i.e. taking them in legal wedlock) not committing illegal sexual intercourse, nor taking them as (secret) lovers. -- Al-Maa'idah (5:4)
“Chaste women from those who were given the Scripture” means, free woman among those who have been given the Gospel and Torah,namely Christians and Jews.
On the other hand, it is impermissible for a Muslim man to marry a Magian (Zoroastrian) woman or a communist woman or an idol-worshipping woman, etc.
The evidence for that is as follows:
And do not marry polytheistic women until they believe. And a believing slave woman is better than a free polytheist, even though she might please you. -- Al-Baqarah 2:221
Therefore in light of the aforementioned verses, if you are a Christian or a Jewish woman, you do not need to convert to Islam to marry a Muslim man.
