Since its lawful to have slave according to sharia.will this constitute zina?
This is a joke, but I will take this seriously because it is worth discussing and full of misconceptions. I'll also put the disclaimer that I am not a scholar so this isn't a religious ruling, but I am a practicing American Muslim so these are my views and they reflect a majority of this country. And I haven't studied this issue in depth because it is irrelevant, because slavery is outlawed worldwide.
Slavery as Western history has portrayed it is not as slavery is meant for Islam. The idea of racist social structures that legitimate mistreatment and withdrawal of basic rights from a human goes against the core of Islam. If a Muslim man owns a slave properly- which is NOT the equivalent of American slaves pre-Civil War (or even after), then technically sex is allowed.
If you want to give this question a fair analysis, study Islamic inheritance and property law. This will give you an idea of the intentions of such beliefs and what it means to have children to inherit your property. If you are looking for ways to demonize a religion and its followers, I'd seriously reconsider your point of attack. This won't work in the long run.
And those I am reading this question negatively, please don't think that I am discouraging questions. Ask me more! I'll either find out for you by studying myself or by pointing you in the right direction. Knowledge is power and I look forward to discussing such heavy topics in a civilized manner.
You cannot enslave a Muslim or non-Muslim free girl. If this is a work around to get sex outside the bounds of marriage, it's a pretty poir attempt.
Bottom line: Get married.