No, he does not have a profile yet, either here at Wikitree or at familysearch.org (the Robert Barnes born 1825 in SC who is profile Barnes-462 is a different one, that one had moved to Alabama by 1850).
The data we have for him is the 1850 census cited above by Betty (living with his presumed sister Rebecca, who had married Leroy/Marion Parish), the 1860 census cited above by Betty (married to Julia, son Robert Barnes age 1, who is presumably your Robert Jackson Barnes), the 1870 census (married to Julia, with son Robert I. and several other children), and the 1880 census (listed as R. Dorsey or Dorcy Barnes, still married to Julia), as well as the 1929 death certificate of son John Barnes (listing Julia's maiden name as Davis). All records from Chester County, SC.
The 1840 census record cited above by Betty (together with the middle name recorded in 1880) suggests he may have been a son of the Dorsey Barnes who was in his 40s and a slave-owning farmer in Chester County. To confirm this we would probably need either probate and/or land records.