Is it common to cite information from a think tank into one's literature review?
Your literature review should include relevant research around your topic. If the paper is just a policy statement, you can ignore it. But if it is based on research by the think-tank you could include it. However, it would be good to indicate a caveat in some way, perhaps just by having a separate section, perhaps with a clear statement. 

Some think-tank research isn't really research at all, of course, but just the gathering of one-sided support for an already decided on position. The caveat given for papers of that sort should be strong IMO. But, since that isn't research in any sense, but just propaganda, you can ignore it with a clear conscience. 

But for a direct answer, I doubt that this is very common except in some fields in which think-tanks generally do valid research. Though a thesis based on the analysis of propaganda would probably be an exception to this rule.