You can bring your Toyota Camry to California and have it registered here as long as its original emissions system has not been tampered with and the Camry passes the CA smog check. It is not required that the vehicle be 50-State California Emissions Complaint; just in case it's a 49-State Emissions compliant vehicle. Your underhood emissions label will indicate whether it is California or Federal (49-state) emissions certified.
As far as the emissions inspection (smog check) itself... your State's emissions inspection program is similar to that of California's; as it's applicable to 2000 and newer vehicles. Your vehicle will undergo an OBD-II systems check only. No tailpipe test. The inspection will ensure the check engine light is not ON, trouble codes do not exist in the vehicle's emissions computer, and all Emission Monitors (readiness monitors) are READY or COMPLETE.
With that said, should you wish, you may obtain an emissions inspection pre-test (or actual test) from your state to ensure your Toyota Camry passes the inspection before bringing it to California. Note... the inspection results in your state will not be valid for use in California. The inspection should only be used as a tool to find out if your vehicle is ready for inspection in California.
We'd like to also add that during the shipping of your Toyota Camry you must ensure the battery does not die, or require charging or changing. If any fault causes the battery to drain or disconnect from your Camry's engine emission control computer, the vehicle will need to be driven 100-200 miles over the course of several days and in both highway and city traffic conditions in order to make the emission monitors ready again for the test. A drained or disconnected battery will erase all emission information from the computer and require resetting.