I heard “I want your sex” on YouTube and the phrase kept bugging me. I realized George Michael had a song titled that way after googling. Is this grammatically correct? I want to laugh at it but I'm not sure...
In George Michael's case, 'your sex' probably means 'your penis'. This is a rather old fashioned usage, sometimes used in novels up to the 1960s or so - 'I touched his sex' because 'I touched his penis' was considered to be too explicit. Of course, it could also mean 'I want to have sex with you'. The lyrics and titles of songs and poems do not have to strictly follow the rules of grammar, as their purpose is mostly to suggest thoughts and feelings. Also, for practical and business reasons, it is usually preferred that titles of songs conform to conventions of decency, etc.
Grammatically correct slang
The Oxford English Dictionary has this definition for sex:
Slang or euphemistic. A person's genitals.
The definition has examples like "The narrow white briefs that barely captured her sex" (1977) and "And he put in a fake sex (penis) because he wanted to make the scene more real, more rude" (2003).
So it is a grammatically correct way of referring to sex organs. It is slang that is not in common use.