I have used Vocaroo in the past - super easy and you can create a QR code as you save the file. However, Vocaroo they will only save your audio files for an unspecified period of time, which means your QR codes on the tests may suddenly quit working. But in this recent post from Richard Byrne at FreeTech4Teachers, he shares about TwistedWave, a site that will record and allow you to export to your Google Drive. Of course, there is still the step of turning it into a QR code, for which I recommend QRStuff, because it allows you to create codes in colors. Great for color-coding by difficulty level, unit, language, etc.
I just tried TwistedWave myself and it worked very smoothly. You'll need to sign up for an account, but it's free (key word for me!)