The 28-year-old defender has been given the armband after regular skipper Garry Monk was ruled out until March with medial ligament damage.
He told Wales Online: "Being captain is something you've got to enjoy and cherish and I certainly do.
"I'm a natural talker anyway, the same as Monks, and that's probably why we are captain and vice-captain.
"I love being captain, but it won't change the way I play."
Tate, a former Manchester United trainee, has helped the Swans into second place in the Championship, just two points behind leaders QPR.