Odey joined the Danish Superliga side from Belgian Jupiler League giants KRC Genk on transfer deadline day.
Genk confirmed, FC Randers have an option to make the loan deal permanent at the end of the season.
Odey joined Genk from Swiss side Grasshopper FC in 2019 and he has struggled to secure a regular place in the squad.
The former MFM FC of Nigeria attacker already spent the 2020-2021 campaign on loan at French second division team Amiens.
His contract at Genk runs until mid-2024.