Coyle, 27, joins younger brother Thomas, who is on loan from Leigh, at the South Leeds Stadium, having started the season at Workington.
The pair have previously played together at Wigan, Widnes and Oldham.
Director of Rugby Darren Williams said: “James started the season in the Workington side but picked up an injury and although now fully fit he has been unable to force his way into Gary Charlton’s line up.
“Thanks to Gary and the Workington club for allowing James to join us, James is a good player he’s a great organiser who can break the defensive line and score tries.”
Coyle will go straight in to the squad for Sunday’s game against Halifax, alongside Clarkson, who is the latest Rhinos player to join the Hawks as part of the partnership between the two clubs.