Here's the answer:
“可以刷卡吗？”
(ké-yǐ shuā-kǎ ma?)
Watch a real native speaker say it:
Here's how it sounds in a textbook:
You could also say:
- wǒ ké-yǐ shuā-kǎ ma?
Fun fact: the hundreds of thousands of people learning Chinese with Memrise get this phrase correct 95.5% of the time!
