If this is a power inverter to provide an AC power source, it will be very inefficient.
Consider using a more efficient high voltage DC generator then using the microcontroller to convert the DC to 'clean' AC.
Your problem with the present design is that with a 4-bit DAC you only get 16 steps in output voltage so the waveform will never be sinusoidal. The best you can do is pass the signal through a low pass filter to limit its slew rate so the sides of the step are less steep. Not a good solution but better than none.
Brian.