I believe there's a spell in The Witcher games that's used for convincing people of things? I'll get around to playing The Witcher 3 for more than two hours someday.

Probably.

Beyond that, the only thing I know of close to what Tedd's describing is in The Elder Scrolls Oblivion (aka the 4th Skyrim prequel). It's possible to craft your own spells in those games, and NPCs have a disposition towards you.

What I would do was to create a spell that would make them like you as much as it's possible to like you for a few seconds (maybe even just one second? Can't remember), then enter dialogue as quickly as possible.

Which possibly sounds evil, but remember, this is a video game in which you can make anyone love you if you're willing to go through a convoluted conversation mini-game enough times. I know I could have stopped at "this is a video game", but the conversation mini-game existing really makes it feel like, if anything, you're doing them a favor. Their faces would totally get sore making so many exaggerated expressions for the mini-game.

Morality aside (something that should only said casually in reference to fiction), I find wizardly mind tricks more believable than "oh my gosh your hat is amazing I bow to will".

All that said, if there isn't something like this in an actual Star Wars game, I am disappointed. And possibly just revealed that I never made it far in Knights of The Old Republic, either, but maybe not? I wouldn't know (but assume I'm about to find out).