The "Oxford Dictionary of first names" has: Rae - Probably a short form of Rachel, now generally taken as a feminine form of Ray or Raymond, or simply a derivative of "ray" meaning sunbeam. [Now the good part!] In some cases it may be a transferred use of the Scottish surname Rae, originally either a short form of MacRae (from a Gaelic personal name meaning "son of grace") or a nickname from the ROEBUCK.
So, it basically seems to come, via the surname, from the Scots name for the Roe Deer. The Scots (not Scottish Gaelic) word for "Roe deer" is actually "rae", as you can verify using this online Scots dictionary (http://www.scots-online.org/).
The etymology of "Roe" is (from Wiktionary): Middle English ro from Old English rā, rāha "roe deer" from Proto-Germanic *raiχōn (“‘roe deer’”) from Proto-Indo-European base *rei- (“‘spotted, streaked’”). Compare Old Norse rá (Danish rå), Dutch ree, Old High German rēho ( German Reh "doe"). So, instead of Scandinavian, I would say Protogermanic, with Scandinavian equivalents (as well as German, Dutch, Frisian...).