yes, your cqa is a regular ar-15, as long as you use the correct length of magpul hand guard it will fit. if you have the 14.5" barrel then you have a carbine length gas system, make sure to buy that, if you have the 20" barrel then you have a rifle length gas system, buy that instead. simple as that.
You might have to trim a little off the front part that sits in the hand guard cap for it to fit. I used a pair of diagonal cutters and trimmed a bit off.
I've circled the bit that I trimmed I did it both halfs of the moe handguard. I did try to put a SL handguard on mine but I couldn't get it to fit over the delta ring.
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