He couldn't have been born in Rockbrdige County because it was established in 1778 from Augusta and Botetourt Counties. However it doesn't really matter because Virginia didn't start recording births until 1853.
If you knew where he was born, you could look for his church baptism record.
Rockbridge County records are on microfilm at the Virginia Library, www.lva.virginia.gov/public/local/results_all.asp?CountyID=V...
. You can look through the list and decide which films you want to view. However your local, public library must request the film via inter-library transfer.
Marriage bonds start in 1778. You'll want to look for their marriage bonds which might have both sets of parents on it. If you can find where and when they married but no parents, then look for their marriage announcement in the local newspaper.
The records also might be available in FamilySearch, Catalog.
Also look for his death record. Virginia started recording deaths in 1853. His parents names might be in his newspaper death notice. Successful Searching!