Double Stack: The estimates lev 3 gave you are pretty much on the money (pun intended). Your rifle is a good one, the caliber is especially nice (and, though not my first or second choice for elk, with the right bullet and some discipline, I wouldn't hesitate on going after one with it) but it is not particularly "rare" and will probably not become an "antique" in your lifetime.
My source (Ruger Model 77 Bolt Action Rifles by Burke), though dated, does stipulate that Ruger introduced the Roberts caliber in the 77s in 1972 "on a limited, uncatalogued basis...a rough estimate would be around two thousand (made during this time period)". These rifles were the ST version, having round-top receivers and sights, with a 24", medium weight barrels. I don't know when this first "run" was terminated but it was at some point in time and was later introduced in the 1975 catalog (according to Mr.Burke,"in the77R version, with a '71'-prefix, 22" barrel, and was made in the '71'-prefix with '200th' year rollmark" but my 1975 catalog indicates that the Roberts was made in the 77RS and ST versions as well). Mr. Burke said that the ".257 was again discontinued in 1976 (though my 1976 catalog shows it being offered that year), only to return again in 1980, in the warning model."
From 1980 on (with the exception of 1999, per the catalog), the Model 77/77 Mark II rifles have been chambered in one form or another (usually the 77R but also the RL and maybe others) in the .257 Roberts caliber.
Hope this helps but keep in mind that most all firearm manufacturers will have some variances in model designations and nomenclatures over time due special orders, inventory left-overs, errors in procedure, etc. It's these differences from the cataloged norms that light up a collector's eyes!