The 33-year-old, who had been a free agent after leaving Scunthorpe United in the summer, also has the option of a second year based on appearances.
"I'm pleased to be able to bring Akpo to Tranmere as he's a player I've been looking at for some time. He's a big, powerful centre forward who leads the line well and can score goals," Tranmere boss Ronnie Moore told the club's official website.
"With Akpo joining Ryan Lowe, Jean-Louis Akpa Akpro and Cole Stockton at the club we have four good striking options available now and they all offer us something slightly different."
Sodje has previously played for Port Vale, Sheffield Wednesday and Preston North End.