Como é que se diz isto em Inglês (EUA)? Ring me up!
When I looked up "ring me up!", I found that it means "call".
Why does it mean "call" when I'm asking for the bill?

See a translation

“Ring me up” is what you say to a cashier.
You are telling the cashier that you are done shopping.
You are asking the cashier to total your purchases and charge you.
Old cash registers made a bell sound.
So the “ring” refers to the sound of a bell as your purchases are totaled.
“Ring me up” isn’t really used for phone calls.
Instead, if you say, “Give me a ring” then it can mean “give me a call”
Again “ring” represents the sound of a bell. In this case, the bell is the sound made by a phone.
Of course “give me a ring” can also mean giving a jewelry ring, so context is important.