Yes of course a Christian catholic woman can marry a muslim. But since this is a major decision in one's life, think over it. Especially in cases where the husband stays/works in a different country than the wife, there've been reported cases where the husband has ditched the wife simply because he got his desires satisfied.

The Quran says, '… (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…’ [al-Maa’idah 5:5]

There're are 3 basic conditions which need to be fulfilled
1. the proposal of your guardian – who may be your father or whoever is acting in his place if he is not there, on the condition that he is of the same religion as you – by his saying, for example, “I offer my daughter in marriage to you.”
2.Acceptance on the part of the husband by saying, for example, “I accept.”
3.The contract was done in the presence of two Muslim witnesses
– then the marriage is valid.

Please go through these links for details.
http://islamqa.com/en/ref/12283/
http://islamqa.com/en/ref/2527

As a general ruling defined from the above verses from the Quran, Women of people of The Book (Jews & Christians) can marry muslim men if they are chaste. Women from other religions than these; eg. buddhism, hinduism etc are not allowed to marry muslim men until they revert to Islam. And do not marry al-mushrikaat (idolatresses, etc.) till they believe (worship Allaah alone)…’ [al-Baqarah 2:221].”

For a clear definition on the people of the book, please see http://islamqa.com/en/ref/300/

Allah knows best.