Energy Harvesting IC datasheet question
Figure 1. Extract from the datasheet.


  
  My input signal is AC 0.8V. Does this circuit allow AC input?
  


According to the datasheet the answer is no.


  
  Is a rectifier included in this circuit? Because I have to convert AC to DC.
  


No.

If you have an AC source you have the option of stepping up the voltage with a transformer. There isn't enough information in your question to comment on whether this is possible.



Update:


  
  The red part uses a transformer to convert dc to ac.
  In my case, omit this part and enter ac directly. 
  If you enter ac in the circuit, will the circuit work?
  


No. Notice that the transformer is 1:100. The FET switches on and creates a DC pulsed current through the transformer. This input voltage is stepped up by a factor of 100 to create a useable voltage on the other side. Feeding 0.8 V directly in will be useless. Feeding a negative voltage into SW will destroy the chip.