Human beings are rational animals. Thus, if a cloned human were truly human, it would have a rational soul.
St. Thomas Aquinas writes in Summa Contra Gentiles, lib. 2 cap. 87 tit. that "the human soul is brought into being through the creative action of God," not through a biological processes, which is only the soul's instrumental cause, but as its efficient cause.
He explains in Summa Contra Gentiles, lib. 2 cap. 86 n. 4-5 and idem, lib. 2 cap. 89 n. 3 why the intellectual or rational human soul is not part of the semen (viz., why the human soul is not bodily but spiritual):
…the intellective soul is the most perfect of souls and its power the
highest [and] its proper perfectible subject is a body having many
different organs through which its multifarious operations can be
carried out; and that is why the soul cannot possibly be actually
present in the semen separated from the body … The intellect, which is
the proper and principal power of the intellective soul, is not the
act of any part of the body, and therefore it cannot be divided
accidentally as a result of the body's being divided [as through cell
division]. Nor, then, can the intellective soul be so divided.
Hence, from the hypothesis that the human soul is brought into being
through the active power in the semen it follows that its being
depends upon matter, as with other material forms. But the contrary of
this has already been proved. The intellective soul, therefore, is in
no way produced through the transmission of the semen.
And the hypothesis of the soul's presence in the semen from the
beginning would entail the further consequence that animal generation
takes place solely by way of partition, as with annulose animals,
where two are produced from one. For, if the semen were possessed of a
soul at the moment of its separation, it would then already be endowed
with a substantial form. But in every case substantial generation
precedes the substantial form; it never comes after it; and if any
changes follow in the wake of the substantial form, they concern not
the being but the well-being of the thing generated. Thus, the
engendering of the animal would be completed with the mere alienation
of the semen; and all subsequent changes would have no bearing upon
the process of generation.
But this theory would be even more ridiculous if applied to the
rational soul. For, first, the soul cannot possibly be divided as the
body is, so as to be present in the separated semen; and second, it
would follow that in all extra-copulative emissions of semen, without
conception taking place, rational souls would nevertheless be
Whenever matter is properly disposed to receive a rational human soul, God creates the human soul out of nothing and unites it with that matter, resulting in a living human being; a human is not just a body or a soul but a body-soul composite.
In the case of human cloning or "test tube babies," the matter (a fertilized human egg) would be properly disposed, and thus God would create a soul out of nothing and infuse it with it at the moment of conception. Just because the means may not have been moral, that doesn't imply God refuses to create a soul; if that were the case, you would have to doubt the humanness of illegitimate children, too.