If someone is “twisting your arm” it means forcing you to do something. For example when a policeman is trying to arrest someone they make them twist their arm behind their back because it is much easier to make someone move in the direction you want them to go when you have control of their arm behind them.

“Hey Paul, are you going to Elizabeth’s birthday party tomorrow?”

“Yeah… I don’t want to go, but she’s really twisting my arm…”