He joined Brid in October from league rivals Barton Town.
Robson is a tough-tackling defender who has travelled the world in his career so far.
The Hull-born 34-year-old has had spells at Charlton Athletic, Bridlington Town, Long Island Rough Riders in the USA, Crystal Palace Baltimore, Newport County, Lincoln City, North Ferriby, Scarborough Athletic and Barton Town.
He becomes the fifth player to make the switch from Bridlington to North Ferriby since Chris Bolder took over as manager.