If you install the Weaver #12 bases, the distance between your rings will be 3". With Picatinny rail spacing at .396 (I think), approx. 2.8" or 3.2" is what would be needed. I have ordered the B-Square 3/8" rimfire rail mounts to replace the #12 bases. I sent an e-mail to the "Tell the CEO" link and customer service on the Ruger website to see if this was by design to not be Picatinny compatible, merely coincidence, or if I had misdrilled holes. Based on the fact they are exactly 3", I don't think it was the latter, and I am guessing not the former, leaving the "coincidence", an oversight in engineering. Anyway, I got an e-mail back within hours from an address signed Michael Fifer (Strum Ruger CEO for those that don't know) telling me great question and he would forward on to marketing and engineering for an answer. I got an answer from customer service (which I think was a reply to my separate customer service e-mail) telling me they would forward to marketing, but didn't actually answer my question.
Anyway, don't bother with the Weaver #12 bases if you intend to share with a Picatinny rail. Will report back on the B-Square bases when I get them, but they should work fine.