Ceramic capacitor value for an LM386N project
You have 10uF between pins 1 and 8.  That sets the gain of the 386 to 200.

200 x 3.3 V = 660V.

You are getting distortion because you are overdriving the 386.

Work it backwards: 

You have a 4.7 V power supply.   You have a gain of 200.  Your input signal can be (at most) 4.7/200= 23.5 mV.

You need to lower the level of your input signal, and reduce the gain of the amplifier.

Reduce the gain:  

Remove the 10uF capacitor from pin 1 to pin 8.  You now have a gain of 20.  That makes a maximum of 235mV before distortion gets bad.

Reduce the input signal:

Use a voltage divider to bring the signal down to 230mV.  From 3.3V to 230mV is a factor of about 14.  So, use a series resistor of 150k between your DAC and the 386.

You also need to put a capacitor in series with the DAC output and the 386.

The DAC has a DC offset different from that of the 386.  This will cause the 386 to push its output off to one side or the other.  Put like a 1uF capacitor in series with the DAC output, before the series resistor.