Im not native english. Is it possible to say "i am veterinarian"? (without the "a")
You should use "a". The word veterinarian can be either noun or adjective, deriving from a Latin word for a person who treats sick (draft) cattle, though now it applies to all animals. As a noun, as with all occupations in English, you must use "a" - a doctor, a teacher, a police officer and so on. You may like to know that in the US the word is usually said in full, but in the UK it is usually rendered in speech and even formal writing as vet. As an adjective, the word would obviously not need "a". As an example, you could say Americans pay a lot for veterinarian services In the UK this would more likely be British people pay a lot for veterinary services where, as you can see, the spelling of the adjective is different.
Hope this helps.
SeanMeanyPL - Both the adjectives "veterinarian" and "veterinary" are utilized in the US. However, the variation in the pronunciation for such word is quite noticeable:
uk /ˈvet. ər. ɪ. nər. i/
us /ˈvet. ər. ə. ner. i/