The signing comes days after the NFL announced that offensive tackle Donald Stephenson has been suspended for the first two games of the 2018 season for violating the league's substance-abuse policy.
Last season with the Detroit Lions, Robinson struggled along with the rest of the offensive line as the team allowed 23 sacks.
Robinson ended up beating out Cyrus Kouandjio in training camp for the left tackle job and started six games for Detroit before suffering an ankle injury. The Lions then waived/injured Robinson, who reverted to injured reserve after clearing waivers.
Before his time in Detroit, Robinson played 46 games for the Rams, who originally selected him in the 2014 draft, starting 42 at tackle and guard.
The Browns waived offensive lineman Rod Johnson in a corresponding move.
ESPN's Michael Rothstein contributed to this report.