Yes, since every living thing has a soul. Plants have vegetative souls (capable of life and growth), animals have sensitive souls (capable of life, growth, and feeling), and humans have rational souls (capable of life, growth, feeling, and rational thought). Only the last kind survives death since only it is made of spirit; souls of plants and animals are made of matter and die when they die.
Since a human clone would be alive, it would have a soul, and since a human clone would be rational and possess a human body, it would have the same sort of soul as every other human. The soul is created directly by God. The human soul is the substantial form and animating life principle of the human body. How you get that body, whether by natural generation, in vitro fertilization, or cloning is irrelevant. God still creates its soul.