In an electrolysis process The rod which is connected to the negative terminal is cathode and the rod which is connected to the positive terminal is anode. So we know that opposite charges approach each rod. Therefore the chlorine ions go to anode as it is the positive charged rod and chlorine ion is negative.
The charges move from charged body to uncharged body because it is the principle of the process. Moving of charged to uncharged body deposit pure form of elements to the depositing rod.