Is it possible to fetch original query's score in rescore query?

You can use a script inside a function score directly in the rescorer:

     "rescore_query" : {
        "function_score" : {
           "script_score": {
              "script": {
                "inline": "_score * ...."
              }
           }
        }
     }

You can access the original score in the script with the special field _score.