The Athletics also announced that right-hander Mike Fiers had been placed on the 10-day IL.
Rosenthal joined the Athletics this offseason on a one-year, $11 million contract, with sources telling ESPN’s Jeff Passan at the time that the right-hander chose the higher annual salary and save opportunities over other multiyear options.
Rosenthal, 30, was 1-0 with 11 saves and a 1.90 ERA in 23 relief appearances last season for the Kansas City Royals and San Diego Padres. He has 132 saves and a 3.36 ERA over eight big league seasons.
Fiers went 6-3 with a 4.58 ERA last season for the Athletics and re-signed on a one-year, $3.5 million contract this offseason.
The Athletics also announced that they had selected left-hander Reymin Guduan and infielder Jed Lowrie from Las Vegas, optioned right-hander Daulton Jefferies and left-hander A.J. Puk to their alternate site, and designated outfielder Skye Bolt for assignment.
Oakland begins its season Thursday by hosting the Houston Astros (10:07 p.m. ET, ESPN).
Information from The Associated Press was used in this report.