In sept of 2006 i was charged with DV but never convicted of it the judge instead gave me a small misidminor and some anger manage classes. I want to apply for the police dept but i dont know if the charge itself will make it so i cant pass the background check?
If you were convicted of anything, even a "small" misdemeanor, it's on your record. You can seek an expungement, but that will not "erase" it from your record - it will only add a notation that the case was dismissed pursuant to the appropriate Penal Code section. In your case, even an expungement doesn't do much, as it does not relieve you of the obligation to disclose it for employment as a peace officer.
The other thing is: You don't say what your "small" misdemeanor was, but you may want to verify whether or not you're disqualified from possessing a firearm. Some misdemeanor convictions carry a 10 year ban on possessing firearms under California state law. Those qualifying misdemeanors include things like assault,battery and any of the misdemeanor domestic violence charges (243 and 273.5). You can find the entire list under Penal Code section 12021.