The 21-year-old centre-back spent the entire 2015-16 season on loan at Cheltenham Town and returned to the Robins for the first half of last term.
His only appearance so far for Reading came as a half-time substitute against Blackburn in May 2016.
"The idea is hopefully that it's with a view to a permanent deal at the end of the loan," said Imps boss Danny Cowley.
"It's something we've been trying to do all window. I'm really delighted to be able to bring Rob into the squad - he's a really gifted centre-half."
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Lincoln City have signed defender Rob Dickie from Championship club Reading in a six-month loan deal.