That's a really good question. I don't ever recall reading anything about a
symbol of
Arnor, but then, I've only read nine of the
books. A strong possibility, though, is the Star born by the
Dúnedain of the North, for I seem to recall that they each bore a star-shaped brooch upon their left (or maybe right?) shoulders. Also, it could have been the Star of the North, also known as the Elendilmir, which
Aragorn gave to
Sam as a gift but which was passed down to the Heirs of
Isildur in the
North Kingdom throughout the history of Arnor and the later among the scattered
Rangers.
Here, I just found a quote about the brooches they wore:
A little apart the Rangers sat, silent, in an ordered company, armed with spear and
bow and
sword. They were clad in cloaks of dark grey, and their hoods were cast now over
helm and head. Their
horses were strong and of proud bearing, but rough-haired; and one stood there without a rider, Aragorn's own
horse that they had brought from the North; Roheryn was his name. There was no gleam of stone or gold, nor any fair thing in all their gear and harness; nor did their riders bear any badge or token, save only that each cloak was pinned upon the left shoulder by a brooch of silver shaped like a rayed star.
So there it is; It could be either the silver rayed-star, or is could also be the Elendilmir, or maybe something else entirely, but those are the only two things I can think of. Of course, there's always the possibility that it is
the White tree and seven stars as well, or something very similar. And also, I beleive (though I may be mistaken) that the seven stars were not part of
Gondor's symbol, but rather the White Tree alone, and both together may have been Arnor, considering that the standard Aragorn bore to
Minas Tirith was of both stars and tree, and he was of Arnor.