He will remain with the Skrill Premier League club until their final game of the 2013/14 league season on Saturday 26 April.
Arthur has made just two first-team appearances for Blues this season, with both of them coming last August.
The 18-year-old Ghanaian links-up with fellow Blues youngsters Charlee Adams
and Nick Townsend
at Sincil Bank.
The midfielder will go straight into Gary Simpson's squad for their trip to Gateshead on Saturday.
The Imps are currently in 12th spot in the table, but just five points off a play-off place.