Anderson, 20, had a 7-5 record with a 2.49 earned-run average for Jacksonville this season.
In 104 2/3 innings, he had 101 strikeouts and limited batters to a .231 average.
Anderson's fastball reportedly tops out at about 96 mph, and he has a better-than-average slider.
The Dodgers' next pick is No. 56 overall. After that, they have the 92nd pick.