Although it is not explicitly stated in Church doctrine, we can determine from related teaching exactly when souls are created and united with their bodies.
First, the Catechism of the Catholic Church (CCC) defines a “human person” as “a unity of spirit and matter, soul and body” (CCC Glossary). So every human person has a spiritual soul.
Also, “[t]he Church teaches that every spiritual soul is created immediately by God” (CCC 366). In other words, souls are not created before or after a human person comes into existence but, rather, immediately at the first moment of the person’s existence.
So, if we can determine when a human person comes into existence, we can also know when his soul is created and united with his body.
When discussing abortion, the Catechism teaches that, “Human life must be respected and protected absolutely from the moment of conception. From the first moment of his existence, a human being must be recognized as having the rights of a person… (CCC 2270; emphasis added). From this we can see that the Church clearly understands the first moment of a person’s existence to be the moment of conception.
Therefore, since (1)every human person has a spiritual soul, (2) spiritual souls are created at the moment a human person comes into existence, and (3) human persons come into existence at the moment of conception, then souls must be created and united with their bodies at the moment conception.
See also: When do identical twins get their souls?