The Giants signed Borders to a contract Sunday, Art Stapleton of The Bergen Record reports.
Borders didn't see the field for the Bears during the 2022 season.
Borders was released by the Cardinals on Sunday.
Borders was activated from the reserve/COVID-19 list Tuesday, Darren Urban of the Cardinals' official site reports.
Borders (illness) was placed on the reserve/COVID-19 list Tuesday, Howard Balzer of SI.com reports, as a result of a positive test, according to Adam Schefter of ESPN.
Borders was waived by the Titans on Tuesday, Joe Rexrode of The Athletic reports.
Borders (hip) agreed to a contract with Tennessee on Monday.
Borders (hip) was cut by the Titans on Thursday.
The Titans placed Borders (hip) on injured reserve Saturday, Aaron Wilson of the Houston Chronicle reports.
Borders (hip) has been ruled out for Sunday's game against the Jaguars, John Glennon of BroadwaySportsMedia.com reports.