Alexander signed a minor-league contract with the Giants on May 3.
Alexander is likely ticketed for Triple-A Sacramento, but he'll presumably require some ramp-up time at the Giants' extended spring training facility in Arizona since he's been on the open market since electing free agency in November. The 32-year-old southpaw finished the 2021 campaign on the Dodgers' 60-day injured list while he contended with shoulder inflammation, but he's presumably healthy now.