After wrongly being convicted of a crime, three hundred years in the future, a former elite soldier is sent to an experimental prison camp on a distant moon, only to be drawn into a violent conflict between an ancient civilization and his fellow prisoners.

I like this concept, only you have to find a way to trim it up

Your story is certainly a good one. Some snips and cuts where the others have suggested would improve your logline.

I'm thinking you might just get away with saying, "drawn into a violent conflict with an ancient civilization" and not really need the part about "fellow prisoners." (given that our protagonist is a prisoner, you've already sort of lead on that it's prisoner vs ancient civilization)

I agree with timmyelliot about the "three hundred years in the future" phrase. It made me think of time travel as well.

I think this is a really good logline. The reader knows who the protagonist is, what the conflict is, and with whom.

I like it.

I don't think you need the phrase, "three hundred years in the future," because that level of specificity doesn't seem necessary to the story (when you were specific about the year, I thought for sure it was going to be a time travel story, which surprised me that it wasn't).