Q. Would a cloned human being have a soul?
A. Biologically speaking, a human clone would be the identical twin of the person whose genetic material was used to produce the clone. The major biological difference between artificially cloned identical twins and naturally occurring ones being that natural identical twins are merely hours apart in age, whereas a cloned twin could be decades younger than his or her identical twin. Another biological difference that would probably occur during the development of the clone in comparison to the naturally procreated individual is that the cloned twin would age very rapidly--the apparent result of using DNA which has replicated numerous times already.
Of course, these are merely physical characteristics of the clone. The soul is not made of just DNA and cellular structures, it is a product of the unique nature of Man, i.e. he is composed of body and spirit. It is the unique combination of these two entities that results in Man's soul. In Genesis chapter two a more detailed account is given concerning how God created Man (Adam) than in chapter one which emphasizes that Man was created in God's image. Genesis 2:7 states, "Then the Lord God formed man of dust from the ground, and breathed into his nostrils the breath of life; and man became a living soul (also translated 'being')." God imparted into the physical part, composed of the "dust from the ground" (which, by-the-way, contains all the elements found in a body), a spiritual part when He "breathed into (him) the breath of life." Notice, then, that it is the result of this combination of body and spirit that "man became a living soul." The soul of Man is the result of his possessing a supernatural entity, his spirit, which is by nature different from his physical body.
So, perhaps, a more specific question to consider when asking whether or not a cloned human being would have a soul is, would a cloned human being have a spirit? We certainly recognize that identical twins are unique persons possessing all the attributes of being human--self-awareness, abstraction, volition, conscience, creativity, etc.--in spite of their genetic identity. They each have a spirit which makes them who they are, and who will exist eternally as persons, either forever in heaven with God and the saints (by faith in Christ as Savior), or forever in hell separated from God. Therefore, if someday Man does produce a human clone which develops full term, is born, and is recognizably alive like any naturally procreated person, surely we would recognize that cloned human being as a unique person, possessing the spirit of Man, and thus, having a soul.
Finally, however, there is the question (which I do not think we can answer) of how is the supernatural spirit of Man passed on to each succeeding generation? The Bible indicates that the spirit is passed on through the male. It was for that reason the Lord Jesus had to be born of a virgin; otherwise the child born to Mary would have received its spirit from Joseph, and could not have been the pre-existent Person, the Son of God. Instead, the spirit of the Son of God was combined with the material seed of the woman, and thus, the Son of God became a human being! Amazingly, this was just like Adam. Jesus possessed a physical part and a spiritual part. Thus, He was indeed fully human. The important difference between Adam and Jesus was Jesus' spirit--that which comprises His Person--existed before He had a body, but that was not the case with Adam. In the cases of Adam and Jesus, God miraculously intervened to combine a spirit with a body, but somehow in normal human conception the spirit is "naturally" procreated and imparted to the newly formed individual. Would such a process occur when Man artificially manipulates the physical materials of cytoplasm and DNA to produce a clone? We cannot know for certain, however, it is my opinion that it would not. We can clone animals because they consist of material substance only, but Man is not just a material being. For that reason, I predict we will not be able to clone human beings, and as long as we are unable to do so, it will remain another testimony to the unique nature of Man who, unlike the animals, was created in the supernatural image of God. If we do indeed someday clone a human being (and I will be very skeptical of such an accomplishment until it is thoroughly verified), the mystery of how the human spirit is passed onto our offspring will be even more challenging to explain.