Hambrick joins former Pittsburgh running back Amos Zereoue, signed last month, as new backs competing to replace Charlie Garner, who signed with Tampa Bay. Tyrone Wheatley and Justin Fargas also are in the mix.
Hambrick became Dallas' starter in place of NFL career rushing leader Emmitt Smith last season, but averaged just 3.5 yards per carry. He gained 972 yards, ranking 19th in the NFL, while starting all 16 games.
The Cowboys cut him last Thursday after drafting Julius Jones in the second round.
Hambrick, an undrafted free agent out of Savannah State, joined the Cowboys in 2000 and has 1,896 yards rushing and 42 receptions.
The Raiders also signed defensive back David Terrell, who spent his first four seasons with the Redskins. Terrell has 188 career tackles and six interceptions.