"drafted a response" is correct and usable in written English.
You can use it when you want to describe the act of writing a response. For example: "I drafted a response to the customer's email in order to address their concerns."
Staff lawyers for Lt. Gen. Ricardo S. Sanchez, the ground commander in Iraq, drafted a response, but General Sanchez was not shown the report until January, when an investigation began.
Jay Carson drafted a response saying, "It's unfortunate that the Bush Administration's TV spin master is manufacturing excuses for North Korea's transgressions instead of looking at the last six years of inaction and the abandonment of diplomacy".
After being queried by the office of the publisher about a possible error, Craig Whitney, who is also the paper's standards editor, drafted a response that was approved by Gerald Marzorati, who is also the editor of the magazine.
Last October, the government in drought-hit Niger – where almost 1 million people are in urgent need of food after a poor harvest – drafted a response plan, focusing on pastoralists, farmers and stocks, in anticipation of a crisis later this year.
Bagenstos drafted a response.
Recognising the needs of the rioters, the Ely magistrates, the Reverends William Metcalfe, Peploe Ward and Henry Law drafted a response, offering poor families two-shillings per head per week and ordering farmers to pay two-shillings per day wages.
Before long, a group of biologists began drafting a response to send to Nature.
Written exercise – analysing a case study, for example, could be drafting a response or business case.
Jacob helped draft a response, explaining and rebutting where he could.
I did try and draft a response against the advice of everybody.
