Here's the answer:
“可以加你微信吗?”
(ké-yǐ jiā nǐ wēi-xìn ma?)
Watch a real native speaker say it:
Here's how it sounds in a textbook:
You could also say:
- wǒ ké-yǐ jiā nǐ wēi-xìn ma?
Fun fact: the hundreds of thousands of people learning Chinese with Memrise get this phrase correct 93.42% of the time!