The 29-year-old was loaned to the Foxes in 2014, when he took 5-34 against Lancashire in the T20 Blast and also played one four-day game.
He is available for red-ball cricket, starting with the County Championship game against Gloucestershire on Monday.
"Richard is looking to get some cricket and fits the bill," said elite performance director Andrew McDonald.
"With some injuries to our seam bowlers in the opening weeks of the season, we needed to add some cover. Richard has previously spent some time at the club, so he's coming into an environment that he's comfortable in."
Stourbridge-born Jones, who has claimed 150 career wickets in 50 first-class appearances at an average of 30.68, will also be available for the County Championship fixture with former club Worcestershire, beginning on 3 July.
Leicestershire signed South Africa all-rounder Farhaan Behardien for the T20 Blast on Thursday.
Leicestershire have signed out-of-favour Warwickshire seamer Richard Jones on a one-month loan deal.