Can a Catholic not married in the Catholic Church but divorced marry a Catholic in the Catholic Church?

Based on the way you worded your question I can only give you a "probably" as an answer. It depends, and I have to give you a multi-part answer to be as truthful as I can be. Catholics are required to marry in the Catholic Church or receive a special permission from a clergy member to be married elsewhere. To not do so is a sin and if this person you speak of exists, they should state this at their next confession. If the previous marriage ceremony you speak of was a civil ceremony only, then without the supernatural grace that comes with a sacramental marriage, the "divorced" Catholic is most likely free to marry a Catholic in the Catholic Church. If the previous marriage ceremony was Christian in nature, its less likely that the divorced Catholic is free to date and marry another - their marriage may be recognized as indissoluble by the Church. The rest of this answer is just advice. Please skip if you don't want it. My advice is have the "divorced" Catholic and their significant other go to a priest or deacon and ask them about being married in the Catholic Church. Catholic clergy are required to do a background check into the eligibility of the marriage. The divorced Catholic will have this previous marriage examined and possibly have to undergo what is called an annulment process. An Annulment is simply a statement that the previous marriage never actually happened and that you are now free to marry again (actually for the first time!)
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Roman Catholic Answer

The above answer is excellent, to be clear, if you were a Catholic married outside of the Church, then the marriage was invalid, and you will probably be able to marry again AFTER you receive an annulment. The Church *always* defends the bond, no matter how invalid it may appear to you, they will look first to see if there was anyway it was a valid marriage. So you will have to apply for annulment, which I am almost sure would be granted due to lack of form: as a baptized Catholic you were required to be married in front of a priest. Simply speak to your parish priest and request the annulment. You may not marry the Catholic until the annulment comes back from Rome, and believe me, it may take some time, so don't make any plans in a rush!