Is it possible to be born with rabies?

No. Rabies is a preventable infectious disease caused by the bite of a animal that is infected eg a dog or bat . its common in tropical countries and can be prevented by being vaccinated against it. .
No. Unless, like Blade, your mother was attacked right before birth. But you would be dead by now...
If pregnant & rabid. A rabid mammal who happens to be pregnant and goes into labor, delivering infected baby mammal(s) before dying of rabies herself . . . Could happen, although it sounds like an uncommon scenario.