Hodge, 22, is the son of former Nottingham Forest and England player Steve Hodge.
Hodge completed a scholarship at Notts County, before signing with Lincoln City on a short-term contract in February 2015 after impressing on trial.
He signed a new one-year contract the following month and made his first-team debut in a 0–0 draw at Dartford in April.
He joined Evo-Stik League South side Stamford AFC on loan and made his debut in a 3–1 defeat at Frickley Athletic in November 2015.
He scored his first goal in senior football in January in a 4–1 Doodson Cup victory over Buxton and made a dozen appearances for the Daniels, scoring one goal.
Hodge joined Gainsborough Trinity on loan in February 2016 and played five games before returning to Sincil Bank.
He then played nine games for the Imps across the 2015/16 campaign and then joined Evo-Stik Premier side Stafford Rangers on an initial one-month loan in September 2016.
He returned to the National League North on a one-month loan at AFC Telford United in December 2016 and played fifteen games for the Bucks at the end of the 2016/17 season, whilst he also featured twice for parent club Lincoln, who achieved promotion back to the Football League as champions of the National League.
He was released by Lincoln manager Danny Cowley in June 2017.
Hodge would then return and sign for Notts County after impressing Kevin Nolan after a trial in August 2017. He then made his EFL debut off the bench for the Magpies in a 1-0 defeat to Swindon in late December 2017.
Reds boss Chris Moyses told the club`s official website: "I've known Elliot for a while now and have worked with him before whilst at Lincoln. He's a quick player, good on his feet. He uses the ball well and will provide us with added pace in the midfield area.
"We are delighted to have him here at the Reds, his preferred position is a winger, but he can play anywhere across the midfield. He will help us in the sense of he's been full time training with Notts County, he's been in this league before and it's good experience for both parties.
"It will be beneficial for Elliot to get games and also for us to have him and have him contribute to the campaign".