A Catholic can marry anyone they wish in a civil ceremony. My mother, who was Catholic, married my father, who was not, this way.
However, their marriage was not recognized by the church. In order to have a recognized marriage, my parents would have had to meet four criteria: (1) the two people are free to marry; (2) they freely exchange their consent; (3) in consenting to marry, they intend to marry for life, to be faithful to one another and be open to children; and (4) their consent is given in the presence of two witnesses and before an authorized Church minister.
In addition, because my father wasn't Catholic, my mother would have had to request permission from the local bishop to marry a non-Catholic. The non-Catholic spouse does not have to convert to Catholicism.
Because marriage is considered a sacrament, the Catholic church also requires the marriage to be performed in a church, or another venue that has been approved by a local bishop.