Can you turn someone in for running a red light if you record it on camera?

Yes! You have great evidence and a traffic infraction can be enforced under the same statute of limitations as other misdemeanor crimes, state to state may vary though.

Additional: (in the US) a traffic violation is a misdemeanor offense. Although in SOME jurisdictions a civilian MAY present the facts of a witnessed offense to a Justice of the Peace or Prosecutor and swear out a complaint - - with very few exceptions (i.e.: so-called 'probable cause' misdemeanors), they MUST be witnessed by a law enforcement officer for any immediate enforcement action to be taken.