Who wrote the United States Constitution?

No one person wrote the United States Constitution all by himself.  We do not even know who wrote any particular section of the document.  If your instructor expects you to actually give a name, it is likely that you are supposed to give James Madison as your answer.  Madison is often called the “father of the Constitution,” but this does not mean that he actually wrote the document.

As you can see in the link below from the US government archives, no single person is credited with writing the Constitution.  People sometimes say Madison did and sometimes say that Governor Morris did.  However, experts are not convinced.  As the link says,

The actual literary form is believed to be largely that of Morris, and the chief testimony for this is in the letters and papers of Madison, and Morris's claim. However, the document in reality was built slowly and laboriously, with not a piece of material included until it had been shaped and approved. The preamble was written by the Committee of Style.

So, we have to say that no single person wrote the US Constitution.  If you do have to give a name, I would suggest that you check to see if your textbook gives an answer to the question.  If so, that is probably the name your instructor expects you to give.