There is no record of his origin, other than the text of the Primary Chronicle by Nestor. And it amounts to:

Thus they went overseas to the Varangians, to the Rus. These particular Varangians were known as Rus', just as some are called Swedes, and others Normans and Angles, and still others Gotlanders, for they were thus named. The Chuds, the Slavs, the Krivichians and the Ves then said to the Rus, "Our land is great and rich, but there is no order in it. Come reign as princes, rule over us". Three brothers, with their kinfolk, were selected. They brought with them all the Rus' and migrated. The oldest, Rurik, located himself in Novgorod;

So that states their origins as Scandinavian, but gives no clue to where. The Scandinavian origins are also reinforced by the name Rurik likely being from Old Norse Rørek, and the first few Rus' kings had other names from Norse like Igor from Ingvar.

The most common theory is that they stemmed from Roslagen (or Roden) in Sweden and that Rus' is a cognate of that name or the related demonym (Norse ros-byggiar) The eastern travels of people from there lead to that name being the origin of the Finnish name for Sweden (Ruotsi) as well as the Estonian (Rootsi). It's well-attested that vikings/varangians from that area traveled eastward and down the Dniepr to the Black Sea and down the Volga to the Caspian. It was mainly vikings from Sweden, and then primarily that east-coast part of Sweden who traveled eastwards.

The chronicle would seem to exclude Swedes since they're mentioned separately, but 'Swedes' as an ethnic group in the present day sense did not exist in Nestor's time, much less the 9th century. Inhabitants of present-day Sweden identified as svear ('swedes'), götar (geats) and gutar (gotlanders), and the former two were subdivided into even more groups, out of which the inhabitants of Roden were but one. Note that Nestor may have mentioned Gotlanders* separately, despite politically being part of Sweden at that time, or at least a Swedish protectorate. (per the Gutasaga) It's not clear how much Nestor knew about these group identities in his own day, much less about those 200 years earlier. (* It's not known for certain if he meant gotlanders, or geats or goths, three distantly related groups with cognate names. Gabriella Oxenstierna's translation of the Primary Chronicle goes with 'goths', the linked one in English uses 'Gotlanders')

Everything you read will be from after they came. The 9th century is well prior to written history in Scandinavia, save for a handful of runestones (and most of those don't say much that's useful in general), none of which mention that Rurik/Rørek or any other one. So there's no written records, but not much reason to believe there would be any, either. Far bigger events went unrecorded; the biggest political event of that era in Sweden was when the Svear and Götar got together into the political union that became Sweden. We have little idea when that happened other than a 6th to 9th century time frame, nor how it happened (i.e. peacefully or through war).

AFAIK, Norway has not been suggested as an origin. Slavic origins have been suggested by Russian scholars, most recently during the Soviet period, but those did not gain much currency outside the USSR. However it's been pointed out many times that even if the Rus' were Scandinavian, there's evidence assimilated quickly, such as already the third generation of Rus' rulers having purely Slavic names.

There are books about varangians and the Rus' (Larsson, Mats G: Rusernas rike. Nordborna och Rysslands födelse, is one source of mine here). I don't know of a book on Rurik alone, and it's hard to see how you'd fill a book on it, given that there's only one source on his origins, written some three centuries later. There are many willing to try though, many fringe theories on this topic out there. Bottom line is that for all we know, Rurik may not even have existed in the first place. It's not a solvable riddle, but Sweden is by most considered the best guess as the origin of the Rus'.