How to detect AC signal and use as logic-level input to microcontroller
Your initial difficulty is that the 7805 regulator has a dropout voltage (below which it no longer regulates) of about 2 V. Look at the datasheet.
This means to get regulated 5 V from your 12 V supply the input needs to be greater than 7 V. 

Your second difficulty is whether you need a simple level detector or more. Since what you show is a half wave rectifier, you will get approximately 0.8 V less than the positive peak voltage.  

If you want an accurate level detection, then you should use a comparator to drive a BJT switch to turn on your 12 V input.

I notice in your comment that you don't need power ...you simply want a signal into an Arduino. Then all you need is a peak detector and comparator, and feed that signal into the Arduino. You wouldn't even need the 12 V supply.