Randolph, who spent last season with Portland, brings the Blazers' roster to 16 players. The league has allowed the team two hardship exemptions in light of a rash of injuries.
Randolph was waived by Miami earlier this year. He played in two games for the Heat, going 1 of 7 from the field.
He played in 57 games with Philadelphia in 2005-06 as a 6-foot-10 rookie out of Duke. But he's appeared in 34 games with the 76ers, the Blazers and Heat in parts of four seasons since.