The rings you have are 3/8" Rimfire rings...for a Dovetail 3/8" base (JUNK)
The base you need for them is junk...way back Ruger used to provide those with a newly purchased 10/22..they changed to a Weaver style but with typical Ruger OEM flare or lack of many moon ago...but it is just barely a decent rail with minimum cross slots.
But, if ya need/want a 3/8" rail I have one for you..PM me and I will mail it...pay-it-forward/no charge.
I suggest a Weaver/Pic Rail but NOT he one you got...you do not need the 15 MOA slope for most applications and only when shooting at distances over the norm.
So..a return on that base is in order...and maybe a exchange depending on what that retailer has...but then you will need new rings..so right now you have nothing that works..you knew that.
In some towns there is garbage on the shelves and a internet order may be needed. But, a great set of rings on the cheep can be had at Walmart = Weaver Quad Locks..Med height will work just fine for you along with a Weaver style rail.
As shown here..but around $12 at Wallies...http://www.amazon.com/Weaver-1-Inch-Medium-Detachable-Rings/dp/B004NCHB9O
This rail is one of my fav's and reasonable....