Trump's remarks alleging his phones were “tapped” are preposterous and reflect his complete ignorance of how the various surveillance authorities retained by the government actually work. The president cannot, on his own, authorize surveillance of a U.S. citizen. Whether for criminal purposes or foreign intelligence purposes, a court order is required.. There is no indication in any of the reporting that a FISA warrant was issued targeting Trump specifically. 

It is more likely the government sufficiently demonstrated to the FISC’s satisfaction that Trump associates might be agents of a foreign power.

Trump is a political and government novice, and this is not the first time he has put his complete ignorance of governmental laws on display via Twitter. It would be in his best interests to start educating himself on the laws and procedures that apply to the government he now runs.