Sodje left previous club Preston last month and is reunited with Iron boss Brian Laws, who signed him during his spell in charge of Sheffield Wednesday in August 2007.
The 32-year-old is Laws' first permanent signing since his return to the club as manager in October.
Sodje, who scored seven goals in 17 games this season after joining Preston on a free transfer in the summer, has appeared for 14 different clubs since signing his first professional contract with QPR in 2001.
He is expected to be included in Laws' squad for Saturday's npower League One clash at Colchester.
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