Translation:The girl is being offered a job as waiter at a restaurant.
"Tjener" (unisex) is more common and more informal and is perfectly fine to use about a woman. "Servitrice" is mostly used by old people and not totally interchangeable with "tjener". There's also "tjenerinde" ("tjener" with female suffix), but again, it adds formality and is largely redundant.
"af en restaurant". "Hun bliver tilbudt et job som tjener af en restaurant." We probably wouldn't say this, though, because it could just as well mean "she's offered a job as waitress of a restaurant". And even though common sense tells us that's not what you mean, we don't appreciate that kind of ambiguity. So, what we would probably say would be: "Der er en restaurant, der har tilbudt hende et job som tjener".