Dating a non catholic
Likewise, your question should be, can a Christian(Catholic) date a non-christian. Just as a quick tweak to the question, Catholics are Christians, so every time you see a couple of Catholics you see a Christian dating a Catholic.
And the answer would be, Yes, and that individual is save through the spouse that is the Christian(Catholic). We can safely assume, however, that the question refers to Protestant Christians. The Church does not prohibit it, but in her wisdom does warn that this is extremely difficult.
Instead, your dating relationship might provide an opportunity to learn about each other’s beliefs.
We indeed may be attracted to a person whose life experiences have been different than our own.
Hearing more about the religious beliefs of a Protestant Christian may help a Catholic to understand his or her own tradition more deeply.
The Church allows such marriages but asks the Catholic to promise that he or she will do all possible to continue in the practice of the Catholic faith and have any children baptized and raised as Catholics.
If the Catholic Church allows the wedding of Catholics and other Christians, it accepts the reality that Catholics and other Christians in a society such as ours will meet and sometimes want to date.