In addition to what has been suggested, "chug", you also have other options

You can use the verb [_down_][1]. Here is an example on [YouTube of people downing drinks][2]. For example, you can say

> He downed his beer.

Alternatively, you could also say ***throw back** a drink*.

> They threw back their shots.

"Throw back" is usually used to describing drinking small volume of liquid very quickly.


  [1]: https://www.merriam-webster.com/dictionary/down
  [2]: https://www.youtube.com/watch?v=maDcQzaeT4o