Usually, with most food, drink and meals, we simply say 'have' - have tea, have soup, have breakfast, have a sandwich and so on. If you do want to use a more precise verb, we use 'drink' for drinks, and 'eat' for food. Soup is considered to be a type of food so, although it's liquid, we say 'eat soup'.

You can say "We ate burgers at Red Robin last night." but most people say "We got burgers at Red Robin last night." or "We had burgers at Red Robin last night." in American English. :) Likewise, you can say "We drank frappuccinos at Starbucks yesterday." but most people say "We got frappuccinos at Starbucks yesterday." or "We had frappuccinos at Starbucks yesterday." I would go with "had" in the context of Starbucks though because people usually buy their drinks but drink them elsewhere. In the case of Red Robin, you can say "got" instead of "had" because people automatically assume that you ate the food at the restaurant instead of taking it home or somewhere else to eat it. :)