The diode in the picture isn't a clamp rather it glues the negative portion of the signal to about -0.7 volts whilst the positive part of the signal rises freely. In effect it tries to self bias the average output after the capacitor to the p-p voltage divided by 2.
Setting the "clamp" voltage to be a tad higher can be done by using a forward biased diode generating +0.7 volts and connecting the circuit diode to this instead of 0 volt.
I'm not really sure this is what you may actually require - if you are trying to digitize a microphone signal to mess with the audio in detail then you'll need an amplifier that just centres the signal to mid-band on the ADC. Alternatively, if you are wanting to just analyse the magnitide of the audio signal in order to trigger an event (without trying to analyse detailed audio signals) then this circuit can be fed thru a loss pass filter to get a dc signal that increases or decreases with audio level.