Ramos pitched in 43 games for the Rays in 2014, making seven starts, and had a 3.70 ERA with 66 strikeouts and 39 walks in 82.2 innings.
The 30-year-old is a former first-round draft pick by the San Diego Padres in 2005 and was traded to the Rays in 2010. He has a career 3.90 ERA.
The Angels drafted Sappington in the fifth round of the 2012 draft out of Rockhurst University.
Sappington began 2014 at Double-A Arkansas before moving down to Single-A (Advanced) Inland Empire. Overall, he went 4-11 with a 6.02 ERA and 114 strikeouts in 113.2 innings in his third year in the minors.
The Rays went 77-85 in 2014, while the Angels were a major-league best 98-64 but lost in the Division Series to the Kansas City Royals.
- Molly Geary