A truck hit me turning left on a red light as I was passing thru the intersection on green and I am at fault?

1) If you get a ticket or summons for this, you could choose to try to fight it in court on the trial date: you could present your side of the story, the state could present its side, a judge will decide who is at fault. As discussed in 2), below, it will be hard (not legally impossible, but hard) to win if the police testify you were at fault: the  police are generally credible and believed on this subject.
(Note: this would actually very likely take more than one appearance; typically, you enter your plea in person the first day, then they schedule an actual trial for a few weeks later.)
2) If you have collision insurance for your own car damage, submit a claim--that's easiest way to be paid for your damage. If you don't, in order to get compensation, you'd have to sue the truck driver and (if it is a different person, including being an LLC or corporation) his employer and/or the truck's owner. You'd have to prove in court that the truck driver was at fault, not you. The police report is NOT a binding legal determination: it is just the police's opinion. So the fact that the police found you at fault does not automatically mean you will lose. That said, it is strong evidence against you; it may be very difficult to   convince a court that you were not at fault if the police say you were.
3) If you are sued for more money than your policy (e.g. liability insurance) will pay out, you could defend in court on the basis you were not at fault. You will run into the same issues as discussed in 1) and 2), above.