The answer to this is going to depend on exactly what you mean by "can" and "own."
Is it legal? No. That is slavery. Is it possible? Yes, it is possible to keep a captive and force him or her to do your will. It is even possible for a person to become a slave willingly and submit voluntarily to another. Is that "ownership," though?
Does "own" mean the legal right to possess, keep, and sell or dispose of at one's will? Then no, not if it has to be legal.
But there have been times and places when it was legal, as you well know, to claim ownership of another human being as property. And there are and have been many things done outside the law.
If you define "own" in another way, however, and there is a lot of room for both gross and subtle variation in the meaning of that word, you may be describing a relationship that is possible and not illegal but that still involves ownership in some sense.