Answer: no
Camera film contains traces of gelatin. Gelatin is most often not vegan, as it is usually derived from animal sources (skin, bones, tissue, organs … yeck). There is always “talk” of a vegan-friendly film supplier, but I have never been able to find it. Your best bet is going to be digital.
Unfortunately, most high end cameras come with leather straps and leather lens pouches. If photography is important to you then you probably won’t win this one.
You could use a large format camera and make glass plate negatives. No gelatin there. Just make sure the camera’s bellows is made of an appropriate material. This method is not for the thrifty.