And as plenty of professionals in security and intelligence have pointed out: no, he couldn’t have.
I think there’s more wrong here in Trump’s thinking than factual ignorance of the limitations of the office. In order to understand that Obama could not have ordered taps, Trump has to acknowledge that he really can’t do it either, should he want to. Trump’s admiration for Putin and things Russian has a good portion of envy of Putin’s autocratic powers in it, and on top of it, his frustration waxes daily at the way Americans, from high level offices to average citizens, can push back when their leader gives them reason to. Putin wants a tap, or even an assassination, he just snaps his fingers —who can tell him “no”? Trump’s recognition of this has become a desire to have the same life and death power. He can’t tell a fact from a wish on a good day; no wonder he would rather believe he’s being tapped than to admit presidents can’t do that.