Which part is the anode of this voltaic cell?

The anode in a voltaic cell is the source of electrons so it is considered to be negative. The counterpart is the cathode, which is considered to be positive. If you look at the diagram the electron flow goes from A to B. This means that part A is the anode. Part B is the cathode. Part C and D is the electrolyte. 

The answer therefore is the first option.