Shaw's agency, North Star Sports Management, announced Wednesday that the 28-year-old agreed to a minor-league contract with the White Sox.
The Orioles released Shaw on Monday, Roch Kubatko of MASNSports.com reports.
Shaw was reassigned to minor-league camp Friday, Rich Dubroff of BaltimoreBaseball.com reports.
Shaw cleared waivers Monday and was outrighted to Triple-A Norfolk, Roch Kubatko of MASNSports.com reports.
Shaw was designated for assignment by the Orioles on Tuesday, Steve Melewski of MASNSports.com reports.
Shaw was claimed off waivers by the Orioles on Wednesday, Roch Kubatko of MASNSports.com reports.
Shaw was designated for assignment Friday.
Shaw joined the Giants' 60-man player pool, Alex Pavlovic of NBC Sports Bay Area reports.
Shaw was optioned to Triple-A Sacramento on Friday, Maria I. Guardado of MLB.com reports.
Shaw went 0-for-3 as a designate hitter in Tuesday's 7-6 victory over the Red Sox.