Katy Perry -- Welcome to ... My Karaoke Rap Show

Katy Perry did her best impression of Will Smith Monday night and morphed into a RAP SUPERSTAR by karaok-ing her way through the classic 90's jam "Welcome to Miami" -- and TMZ has the footage.

It all went down at a karaoke joint on Catalina Island called El Galleon ... Katy went up on stage under the name "Katherine" (smooth), along with another female friend of hers, to get jiggy with Smith's 1998 tune.

The footage is pretty great ... the pop superstar gets most of the words right and even manages to put her own twist on it by saying things in a really high voice -- which was interesting.

It's unclear if Katy was inebriated or not -- it did take place in a bar -- but at the end of the rap she does shout out "I looove my best friend" in a VERY happy way.

Bienvenidos a Catalina!

7/18 -- The day after the karaoke sesh, Katy hit the beach ... and TMZ has obtained some shot of Perry in her bikini. Enjoy!