I'm a newbe here but I'll throw a few suggestions in for you to try. Most times I use a Bore sighter and line up my scope, with that the results are satisfying to me anyway. It sounds like the scope rings are out of adjustment with the barrel, if the rings have tightening screws on each side it may be that one side is screwed in/out moreso than the other side is which is throwing the scope out of alignment. I've found that to be the case 9 out of 10 times, by comparing the scope alignment with iron sights, normally the iron sight picture is what it should be not the scope picture. Maybe I haven't helped much here, but it's pretty hard for me to explain something at times. I would just keep adjusting the scope rings until it came into the general location that the iron sights do and then adjust the elevation/windage on the scope itself when I get to the range to fire the rifle.