You can go to the VA web site---www.va.gov--- In the left hand column click on Burial and Memorials, and in the drop down menu click on headstones and markers. Download VA form 40-1330. Instructions for completion are also on the Headstones and Markers page. Complete the form, attach documentation that your ancestor was a Civil War Vet--pension application or even a widows pension application or other documents verifying his service-- and put it in the mail. VA responds to these marker applications faster than you would think.
Hope this helps.

Ray