I suppose that much depends on how old your child is. I'll assume for the sake of an answer that he's in the 8-11 age range (if he's younger, then I think possibility a -- see below -- becomes more likely; if he's older, then b is more likely)
If I were you, I'd start by asking him why he thinks that acting out will get you back together.
I think there are two possibilites here:
a) He really thinks this will help to reunite the two of you. I find this weird, but who knows what goes through his head. So if that's the case, you need to explain to him that sometimes adults are better off not spending all their time together any more, and that this has nothing to do with him. No matter how he behaves or what he does, it wasn't the reason for your separation and it certainly won't be a reason for reuniting. I don't think you need psychological support for this unless it gets worse once you've talked to him. It might be smart for both of you to talk to him, and both of you to tell him the same (hopefully true) things about why you can't live together any more, and that he didn't, couldn't and won't influence this decision.
b) Here's another possibility: He's a kid, not stupid. He knows that on some level you feel bad about splitting up his family, and he's using this as a way to get away with acting out without having to deal with the fallout. (He may be acting out because he's angry and sad you're no longer living together and doesn't know how to handle it, or it might be completely unrelated - but I wouldn't automatically assume that he's telling you the truth when he tells you he's acting out because he expects it to reunite you).
Of the two, I wouldn't discount possibility b) out of hand. My parents separated when I was about 8 or 9 and I understood early on that this gave us kids some power in dealing with our parents. I don't think we ever misused it, and I don't think we would have gotten away with outrageous behavior or demands, but still, I knew both my parents felt bad about breaking up the family and would make some allowances because of it.