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.

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