The Development Squad midfielder joins the Isthmian League Premier Division outfit on a one-month loan deal.
Widdrington joined Rovers in the summer of 2018 from Portsmouth and progressed to make his first-team debut as a second-half substitute in a Checkatrade Trophy fixture against Exeter City back in November.
Bognor have a busy month of festive fixtures scheduled, with games against the likes of Whitehawk, Lewes and Corinthian-Casuals all in the diary during Widdrington's loan deal.
The 19-year-old midfielder will be eligible for Bognor's encounter with Worthing this Saturday.
Everybody at the Club would like to wish Theo all the best during his time away from the Memorial Stadium.