The phrase is metaphorical and doesn't involve actual physical twisting of someone's arm. She said she would never go camping but we managed to twist her arm.
Pro Tip 2/3
Social Pressure
Often used to imply that the persuasion involved social pressure or a feeling of obligation rather than force. His colleagues twisted his arm into attending the office party.
Pro Tip 3/3
Friendly Persuasion
The phrase can imply a friendly and light-hearted persuasion, not a serious or threatening one. After much chat and laughter, they finally twisted my arm to join the dance.