Record Audio with an Electret Microphone

I am trying to record and save audio files on my PC

Wire it to a 3.5mm plug and plug it into your soundcard. Electret mics require power and your soundcard will provide 5V out of the mic-input.

Is it possible to do this with an Arduino Uno

No. The Arduino is too slow, plus you'd need a preamp and you'd have to write a driver.