(would you) care to join me/us informal question
To give an invitation for one to join in an activity with someone else (or a group).
Would you care to join us for dessert and coffee?
Would you care to join us for dinner this Sunday?
I'm going camping this weekend - care to join me?
An unexpected last-minute invitation
To invite someone to have dinner at a restaurant and pay for the meal.
If you fall for someone's trick the first time then they are at fault.
Are you going to mess with me again? Fool me once, shame on you; fool me twice, shame on me.