Nightcrawler, the superhero identity of Kurt Wagner, is a member of a fictional subspecies of humanity known as mutants, who possess an X-gene that can cause possible physical mutations and in many cases grants some form of superhuman ability.

Warning: contains spoilers for X-Men Blue: Origins #1 Finally, after decades of speculation, Marvel has canonically confirmed that the X-Men hero Nightcrawler is the biological son of Mystique and her wife Destiny, twisting Kurt's birth story into a tale of tragedy and possible redemption.

The short answer is yes, on some level, Nightcrawler is recognized as a mutant, but simply stating that he is only a mutant does not reflect the full story of his background.

Kurt Wagner/ Nightcrawler has been a fan-favorite member of the X-Men ever since he joined the team in 1975's Giant-Size X-Men #1. That book brought together a new team of international mutants as Professor Xavier's new team of heroes, replacing the original five founding members and kicking off a new wave of popularity for the X-Men.