Alright, here's how this goes...
Shield Defense (Ex): Starting at 3rd level, a viking learns the art of fighting with a shield. Whenever she is wearing medium, light, or no armor and wielding a shield, the viking’s shield bonus to AC increases by 1. Every 4 levels thereafter (7th, 11th, and 15th), this bonus increases by 1.
My question is this: would this bonus work with a ring of force shield?
This ring generates a shield-sized (and shield-shaped) wall of force that stays with the ring and can be wielded by the wearer as if it were a heavy shield (+2 AC). This special creation has no armor check penalty or arcane spell failure chance since it is weightless and encumbrance-free. It can be activated and deactivated at will as a free action.
The ring must be wielded, so you're clear there.
"as if it were a heavy shield". Ok, this is going to be a GM call. It's not a heavy shield, but it's wielded as if it is.