Martis arrives on a one month loan deal, and the Baggies have given him permission to play in the FA Cup tie against Preston on Saturday.
The Dutch centre-back may be forced straight into the starting XI, giving Ian Baraclough a rest from the side.
Tony Mowbray's side signed Martis from Scottish side Hibernian in a £50,000 deal in the summer, having previously worked with Mowbray at Easter Road.
"Opportunities have been hard to come by for Shelton here so far but I particularly like his qualities," explained Mowbray.
United draft in Martis
"We need to see him play Championship football. Hopefully, he'll get that opportunity at Scunthorpe and will come back really competing hard for a place in the first team."