Signed by scout Danilo Trancoso, De Los Santos began his professional career for the Texas Rangers organization in 2006, playing for the Dominican Summer Rangers. That season, he appeared in 13 games (making four starts) and went 0-1 with a 1.59 ERA, striking out 48 batters and allowing just 16 hits in 34 innings. He split 2007 between the Dominican Summer Rangers and the AZL Rangers, starting three of his four games and going 0-1 with a 4.32 ERA. In 2008, De Los Santos pitched for the AZL Rangers, going 0-2 with a 4.67 ERA in 10 starts, striking out 54 batters in 34 2/3 innings. The following year, he went 1-1 with a 1.41 ERA in 22 relief appearances for the Dominican Summer Rangers 2, striking out 70 batters in 32 innings. Pitching for the Spokane Indians and Hickory Crawdads in 2010, De Los Santos went 4-2 with a 2.94 ERA in 19 games (13 starts), with 112 strikeouts in 70 1/3 innings.