Get has several meanings, in the general sense of "acquire" for example, it could be:
Get hands on
Those words meaning that you "get" something by buying it (more often than not). You could also "get" something as a gift, with someone else "buying it"
"I will get you a drink!" Gee, thanks, but save your $10 or however much that overpriced cocktail is
In other context get could mean "I´ll fetch a drink for you", but here it means I will buy you a drink" (the offer here is declined, and the mention of the price gives the clue about "get" meaning "buy".)https://www.thesaurus.com/browse/get/2?s=t
One more sentence on the side here, for you.:"I'm going to get you to drink." No, you're not, the same way I'm not going to get you not to drink. People get to make their own decisions, and trying to change mine on alcohol will be a failed endeavor.
"I'm going to get you to drink." meaning "eu vou fazer, eu vou conseguir fazer você beber...
Again, the site makes the point that one may have the willpower to decline, it´s up to one whether to drink or not, but not to others talk you into doing it per se.