"We've signed Elliot for an initial month because we were left without a recognised right-back," Parkinson told the club's official website.
"Elliot is a good young player, and he has impressed us this week, in training and in the reserve game against Dagenham & Redbridge on Tuesday."
Although technically recruited on loan from Fulham until December 1, Omozusi is actually out of contract.
"The situation is a bit complicated because Fulham still hold his registration, so it's not a normal loan," Parkinson continued. "We've had to take him on a month contract, but we also have the option to make it permanent in January."