Its not neccassarily a scope problem. Their could be a pressure point on the barrel that is sending it off. This could also worsen as you shoot more often due to the heat change of the barrel. Also, allow the barrel to cool between shots. Hot barrels can shoot very, very, poorly (discovered that with my 270 WSM!)

most likely it is a scope mount, could be as said above. Ruger makes a quality product. And all mine are very accurate. I have five rugers, and they all shoot great. Re-mount your scope. check for damage, and use locktight. it is great!
-Jake

Check the forearm, and make sure the screw is tight. This happened to me once and I was blaming the scope rings too.

In addition to the things mentioned above it might just be that the rifle does not like the ammo that you are feeding it. If everything else is ok with the rifle, then you may switch the kind of ammo you are using.

I have a ruger 06 and no problems with it. shoots great

Just another voice saying its gotta be the scope/mounts. I own a '06 and i love it.

Don't stress, just hunt with the .243 this year or until you get the .30-06 fixed. I'd hunt with the .243 even after the .06 was fixed.

scope problem....

I dont want to sound like Im making any assumptions about your shooting but just to interject a possible alternative, to just having loose or bad scope, could you possibly have developed a flinch? I know I have at times w/ the heavier 30 cals like the 30 06, which is a huge step up in recoil from a 243. I would stick w/ light 150gr loads. Also get yourself a snap cap and do some dry firing to practice your trigger control.
Ive owned a couple of 77s and although they as solidly built rifles, their triggers are typically heavy w/ alot of creep(overtravel)a big help may be to have a trigger job done or get an ,easy drop in ,aftermarket trigger like rifle basix to lighten up your trigger pull which will tighten your groups aswell. Good luck!

edit mistake