Kapinos will replace the injured Daniel Sepulveda, who was put on injured reserve with a torn ACL.
He beat out Ricky Schmitt in a tryout with the Steelers on Monday.
Sepulveda, who caught his cleats in the turf Sunday night in Baltimore, missed the 2008 season with the same injury after getting hurt on the first day of training camp.
Sepulveda ranks seventh among NFL punters with a 45.5 yards per punt average and is ninth in net punting with a 39.1 average.
James Walker covers the AFC North for ESPN.com. Information from The Associated Press was used in this report.