He is descended from a Thomas Rigsby who was born about 1760 and lived in Mecklenburg Co NC and Warren Co TN. This may be the same as the Thomas Rigsby who married Margaret Williams in Frederick Co VA in 1787, but I'm not certain.
I can pretty much guarantee that almost all the Rigsbys in America are from a family in England who probably were from the Lancashire area. My research goal is to get all the American Rigsby families straightened out.
There were three early Rigsby immigrants who arrived in VA from England: Thomas in 1623, James in 1637, and John in 1695. Just from the names I would guess your Thomas is from the immigrant Thomas, but that's just a wild guess. I haven't been able to track these three immigrants past their arrival date.
There were some other Rigsby immigrants in the 1800s, almost all from England. The few others were from Ireland, apparently from a branch that stopped there first.