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you should use the Ruger base and the any weaver or picatinny rings will work just fine https://shopruger.com/Ruger-American-Rimfire-Scope-Base/productinfo/18156/

Marguarite, you have a choice. I would highly recommend the one piece mount/ring for scope mounting : https://www.budsgunshop.com/product_info.php/products_id/55447/game+reaper+ruger+american+rimfire+mount+normal+action+medium+height+1+inch+matte+black --------------------- Since the Ruger uses a high crown 3/8″ dovetail, these particular rings are a great option : https://www.budsgunshop.com/product_info.php/products_id/723007145/ncstar+1%22+rings+3%2f8%22+dovetail%2c+high%2c+black ------- Details of mount options (just scroll down here) : -- https://warnescopemounts.com/ruger-american-rimfire-mounts/