She had a tattoo done before she became Muslim. Is she cursed?

The Muslim must realize that Islam erases any sins that came before it, and indeed Allaah changes them into good deeds, as He says (interpretation of the meaning): 

“Except those who repent and believe (in Islamic Monotheism), and do righteous deeds; for those, Allaah will change their sins into good deeds, and Allaah is Oft-Forgiving, Most Merciful”

[al-Furqaan 25:70] 

It was narrated that ‘Amr ibn al-‘Aas said: When Allaah put Islam in my heart, I went to the Prophet (peace and blessings of Allaah be upon him) and said: “Give me your right hand so that I may give you my oath of allegiance.” So he held out his hand, but I held my hand back. He said, “What is the matter, O ‘Amr?” I said, “I want to make a condition.” He said, “What is your condition?” I said, “That I be forgiven.” He said, “Do you not know that Islam wipes out whatever came before it, and that hijrah (migration for the sake of Allaah) wipes out whatever came before it, and that Hajj wipes out whatever came before it?” 

(Narrated by Muslim, 121). 

This hadeeth indicates that whoever becomes Muslim is forgiven for all the bad deeds that he may have done before he became a Muslim. 

Secondly: 

It was narrated from the Prophet (peace and blessings of Allaah be upon him) that tattooing is haraam (forbidden). 

It was narrated that Abu Juhayfah (may Allaah be pleased with him) said: “The Prophet (peace and blessings of Allaah be upon him) cursed the one who does tattoos, the one who has a tattoo done, the one who consumes riba (usury or interest) and the one who pays it, and he forbade the price of a dog and the earnings of a prostitute, and he cursed the image-makers.” 

(Narrated by al-Bukhaari, 5032). 

Tattooing is a major sin, but if a person repents from it, Allaah will accept his repentance. 

Thirdly: 

Modern medicine is able to remove tattoos; the remedy exists so you can easily get rid of it, in sha Allah. 

Fourthly: 

The curse of the woman who does tattoos is not permanent; rather when a person repents from it, that curse is lifted. So it is a mistake for you to say that you are a cursed woman. Rather we ask Allaah to make you good and righteous. 

Fifthly: 

Undoubtedly the one who wants to marry you will understand this issue, especially that it was before you became Muslim. Even if it was after you became Muslim, so long as the Muslim has repented from it, he cannot be blamed or called to account for it, rather his bad deeds are changed into good deeds. 

And Allaah knows best.