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Robert, you will need the Ruger Mounting Plate : https://www.budsgunshop.com/product_info.php/products_id/120918/ruger+90720+aluminum+matte+black+hardcoat ------------ And I recommend the Burris Fastfire : https://www.budsgunshop.com/product_info.php/products_id/79681/burris+300236+fastfire+1x+21mm+obj+eye+relief+matte+black -------------------- Install details here : https://www.youtube.com/watch?v=ZvHmtqufJIo

The Ruger Optic Adapter Plate supports the use of Burris FastFire and Vortex Viper/Venom red dot sights on the Ruger-57 pistol. The plate is precision CNC machined from 6061-T6 aircraft aluminum with a matte black hardcoat finish for strength and durability. Simply place the adapter plate onto slide and secure it using the two #6-32 screws provided. Tighten the screws firmly (30-50 in-lbs.) using a Torx T-15 wrench (not included). Install the optic onto the Adapter Plate by following the sight manufacturer's mounting specifications (sight not included). The Adapter Plate is 1.700" long x .975" wide. Made in the USA. As far as Red Dots you've got a few options to choose from.

As others have said you will need item number 736676907205 just type the item number into buds search and it'll pop up. Hope this helps.