Parsons spent two seasons on Oakland's practice squad after the Raiders signed him as an undrafted free agent in 2010. He appeared in all 16 games in 2012, opening the season as the team's starting center. The 6-foot-4, 301-pounder was waived during final roster cuts last year.
Parsons started 21 consecutive games at right guard as a junior and senior at Southern California.
Rogers, who kicked in college at Cincinnati, originally signed with New Orleans as an undrafted free agent in 2011. He spent time with the Saints, Tampa Bay, Dallas, the Giants and Washington, but has not appeared in an NFL regular-season game.
He appeared in four preseason games with Tampa Bay in 2011.
The Browns open a three-day mandatory minicamp on Tuesday.
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