In corresponding roster moves Monday, left-handed reliever Grant Dayton was claimed by the Braves and right-handed reliever Josh Ravin was designated for assignment. The Dodgers have a full 40-man roster.
The Rule 5 Draft will take place Dec. 14 at the Winter Meetings in Lake Buena Vista, Fla.
Santana is the organization's No. 12 prospect, according to MLBPipeline.com, and Oaks is rated as the No. 14 prospect.
Oaks, 24, spent most of 2017 with Triple-A Oklahoma City, going 4-3 with a 3.64 ERA in 16 games (15 starts) with 72 strikeouts against 18 walks in 84 innings.