Yes, there is a difference. "Did you read" is simple past tense, and "Have you read" is present perfect tense. They are very similar, but "have you read" is what you'd more likely say if there is no specific period of time when the act of reading may have occurred, whereas "did you read" is what you'd more likely say if there is a mutually understood time period when the reading may have occurred. (Although I suppose both could be correct in either circumstance, perhaps. Either way, here is a list of differences between simple past tense and present perfect tense.)
The question is, does Korean also have a present perfect tense that corresponds to the English present perfect tense? If so, then I'd say "Have you read" is good English but not a good translation because the Korean is in simple past tense so it should be translated in the same simple past tense. However, if Korean only has past tense and that corresponds to both simple past and present perfect in English, then "have you read" is a correct translation and not just a correct English sentence with roughly the same meaning.