Probably from Scandinavia, where people take their father's name and add son or daughter. For instance, Peterson, Jakobson, and so on.
Very possible, but it can't go unnoticed that Roberts (short for Robertson) is very prevalent in Wales which is Celtic.
Another Answer:I would think it would be English or Scottish.
The Scots even have a Gaelic form of the name: Robasdan. They are called "Na Robasdanaich",as well as "Clann 'IcDhonnchaidh" and "Clann Donnchaidh".
The name Robertson is Scottish. I know so because my name just happens to be Robertson and that they were kicked out of Scotland. Plus my granddad has had our history checked up on and it proves that we were Scottish at one point in time.
Kimmy Robertson's birth name is Kim Robertson.
Si Robertson's birth name is Silas Robertson.
Stan Robertson's birth name is Stanley Robertson.
Allison Robertson's birth name is Allison Rae Robertson.
Antoinette Robertson's birth name is Antoinette Nicole Robertson.
Britt Robertson's birth name is Brittany Leanna Robertson.
Calista Robertson's birth name is Calista Kazuko Robertson.
Erick Robertson's birth name is Erick Joseph Robertson.
Geoffrey Robertson's birth name is Geoffrey Ronald Robertson.
Monroe Robertson's birth name is Monroe Arthur Robertson.
Oscar Robertson's birth name is Oscar Palmer Robertson.
Shirley Robertson's birth name is Shirley Ann Robertson.