Yes, but in the singular, it should be "a". I haven't got a girlfriend as of yet or I haven't got one as of yet.
In the plural, you can use "any". I haven't got any girlfriends as of yet. I haven't got any as of yet.
Student or Learner
Can I say "I haven't got any(Any girlfriend) as of yet". Can we use "Any" for Humans in this way.
How many girlfriends do you want? It sound like you plan to collect them.
I'd suggest, "I don't have a girlfriend yet." or "I haven't had a girlfriend yet." The latter emphasises that you've never had a girlfriend, whereas the former doesn't necessarily have that meaning if the context is right.
I've always seen "as of" as being pointless and often ambiguous. Does "I've had two girlfriends as of early May" mean that you had had two girlfriends up until then, or since then? Yes, it means both or either to different people.