Does the Church believe in the idea of having a soul mate for marriage?
It depends on what you mean by the term. Without an explanation of your understanding of the term, I can only offer general remarks:
Love is an action of the will, and is a choice to want for the beloved that person’s ultimate happiness (God). Thus, it is not strictly necessary for a married couple to have the romantic feelings for each other that people generally consider to accompany being “in love.” Those feelings draw the couple to each other, make the marriage more pleasant, and can ease difficult times for the couple; but the feelings alone cannot be depended upon to sustain the marriage because feelings are fickle.
If, by “soul mates,” you are asking if the Church recognizes that a married couple may have reason to believe that God made them specifically for marriage to each other, the Church does not discount that possibility. The Church also does not discount the possibility that God, in his omniscience, might also have made one of the partners for marriage to another person after the death of the first spouse.
If, by “soul mates,” you are asking about the popular theory that a person only has one other person in the entire world with whom he or she can possibly make a good, holy, and satisfying marriage, and if he or she doesn’t cross paths with his or her soul mate then that person is doomed to lifelong unhappiness, the Church doesn’t teach that. It is a theory popularized by romantic movies and books but does not hold true in real life.