The encounter was filmed by a woman who was a few cars back in line and wondering why it was taking so long to get her food.
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In the video, the restaurant employee can be seen hanging out the window and holding the hand of a driver as she laughs and chats with him.
"Yo, what's going on with the food?" a man in line yells out at her.
"I'm correcting an order," she replied. "That's what I'm doing."
After some back-and-forth comments, the employee tells the frustrated customer, "If you're gonna be rude, I'm not gonna take your order. You can go ahead and leave. I'm not gonna take your order."
As the whole exchange unfolds, she continues to hold hands with the driver at her window.
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The incident happened in September at the Jack-in-the Box at Rosecrans and Woodruff avenues in Bellflower, according to Instagram user @ruthillea.
She says she eventually just drove off, not wanting to spark a further confrontation.
But she posted the encounter to Instagram and sent the footage to the restaurant owner.
She says the owner apologized and offered her some coupons - which she didn't accept.
The owner also told her the "relatively new" employee would not be working at the restaurant much longer.
The cashier told KABC that she has not been fired, and that video will show she did nothing wrong.