”Ha tid” it’s the same as English ”to have time” as in ”Do you have time to look at it?” except that you include it when you specify the unit of time as well so it literally means ”do you have time (for) a minute”.
As a native English speaker and TEFL teacher I don't think "Do you have time for a minute?" is a meaningful English sentence. "Can I have a minute of your time?" is meaningful.
Perhaps, although I'm a native, American-English speaker, my language studies have made me too flexible in some ways. I think both of these are meaningful. The second, "Can I have a minute of your time?" is much clearer and preferred. The former, however, is intelligible and sensible. I'd probably hyphenate it thus: "Do you have time — for a minute?" The grammar doesn't quite mesh, making it sound as if the last clause is separate, an afterthought, but still perfectly sensible in context.
What, then, does "Har du en minut?" mean, if anything? I am going to suspect that 'ha tid' or 'har tid' (in this case) is going to be a construct that has to be remembered when asking about having a time quantity. Yes?
Sorry about the late answer. You can skip tid but it's more idiomatic to keep it. We also often use this kind of sentence without specifying the amount of time, just saying Har du tid?
You could also say Har du en minut över? – closest translation might be 'Do you have a minute to spare?'