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

You can use the verb down. Here is an example on YouTube of people downing drinks. 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.

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

You can use the verb down. Here is an example on YouTube of people downing drinks. 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 describe drinking small volume of liquid very quickly.