The son of Liverpool manager Brendan, Anton has played a key role in the heart of midfield for Luke Williams’ development squad this season, but will now have the chance to sample first-team football.
City have enjoyed a successful campaign which sees them in the play-off places, three points off automatic promotion in fifth place.
The central midfielder will be eligible to make his debut when the Grecians travel to Rotherham at the weekend.
Development squad manager Luke Williams praised the young midfielder’s football nous before the player embarks on his loan move.
He told seagulls.co.uk, “He wants to go and prove himself to the club and also to himself. As a player I am a massive fan as I work with him day in day out and see his quality.
“He understands football and how to create space for his teammates, he knows how to be unselfish and he understands how to break teams down and when to press.
“Tactically he understands football because of the upbringing he has had with his dad and the 24 hour hours a day football, which has clearly rubbed off on him.”
Rodgers has made one senior appearance for Albion, as a substitute in the FA Cup against Wrexham at the Amex last season.