I have a Ruger 10~22 with the scope that came with the rifle in a package deal. Not a great scope but irs fine for me. My issue is that it has a bit of play.... the scope will move a very tiny bit lengthwise on the rail. Everything is tight and it doesn’t impact the accuracy very much, but it shouldn’t have any play at all. It just moves a teensy bit, but it does move. The screws are as tight as they will go.

Any suggestions? I thought about putting something thin on top of the rail, then mounting the scope on top of that. But that doesn’t seem like a great solution.

Long shot but sometimes the small blocks on the bottom of the rings that engage the rail are installed wrong, try turning them over and tighten it down. I have had a couple that looked the same but the angled part was slightly different and they tightened up good when flipped over...

Get better rings.

Unless your'e saying the rings are moving on the rail, which I totally believe as well. The factory rail and rings are pretty bad on the 10/22. If that's the case, I'd look at new rings and a new rail. They don't cost that much. I just did this with my 10/22.

Most package rings and scopes are crud. Also don’t tighten them as much as you can