I think grammatically in English that would be incorrect. Because time always 'exists', you/a person may not have time to do an activity but it exists none the less.
So a more appropriate translation could be: I do not have time.
Meaning if someone asked can you buy me bread on your way home? The response could be: I don't have time I won't be able to buy it.
Shivani, do remember that "var" means, is the equivalent of "it does exist"="my time exists"and that "yok" is the equivalent of "it does not exist"="my time does not exist". It a is way of understanding the construction of the Turkish sentence. Here the Duolingo English sentence is definitively "i do not have time".
Mariane, Yes I think I agree. Although, in the context 'var' for zamanım var it would still mean - I have time. Because literal translation can mean something very different from what the context is trying to convey. It's just that I understand better that way, but what you said makes complete sense. :)
If an English speaker says "I don't have the time," it can mean either "I am too busy," or "I do not know what time it is." If you eliminate the article "the" and just say "I don't have time," it always means too busy.
This is a really good question, English articles are tricky.