I was a little skeptical, but the Twitter checkmark says "This account is verified because it is a government or multilateral organization account", so it does appear to be legit. Bit confusing since he also uses @SenTedCruz--that one seems more professional, so I assume that's run by staffers and @tedcruz is just unadulterated Fox News brainworms.

Pretty sure it is, check recent tweets; they're all Trump campaign stuff.

Pretty sure the real one mentions the fact that he's a Senator