SPOILER ALERT:
Sasuke first met karin in the forest of death during the chunin exam, but you first see them "meeting" each other two episodes after sasuke kills orochimaru.
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chapter 395 somewhere around there Karin first meets Sasuke in the forest of death. She was a genin from another village and was attacked by a giant bear. Then sasuke used shishi rendan or lion's barrage and ko'd the bear. then young sasuke and old sasuke both say see ya. then sakura saves her.
Karin was hurt by Sasuke's attack when they met. She see bright and warm chakra of Naruto and said it was the exact opposite of Sasuke's chakra, which was dark and cold. Then she looked deeper and saw the chakra of the Nine-Tailed Demon Fox.
She appears in the magna and in the anime sometime around Pervy sage's death
I have read as far as the manga goes online, so up to 478, I believe, and so far no. Karin is watching from the sidelines as usual as Sasuke fights. She tried to help him but got kicked away with no effort. She is proving to not even know how to fight. Sakura, is on her way to where Sasuke is now, so if they did fight it would happen soon but I doubt it will be much of a match if Karin really is as weak as she's being portrayed right now. But who knows.
Actually, he has shown no affection for either of those girls. In the Manga, Sasuke is shown to have used Chidori Sharp Spear through Karin to try to kill Danzo. (Danzo was choking Karin from behind.)