Will this lenses work with my Canon T31?
Yes, this Tokina "FX" lens will work on all Canon cameras except the mirrorless models. The Tokina 16-28 mm lens is designed for optimal use on a full-frame (FX) sensor camera, but will work on the Rebel series cameras that have an aps-c sensor. The net result is that the 16mm wide angle end of the zoom range becomes about 25mm (not a real wide angle compared to 16mm) and about 45mm at the 28mm setting.
You could alternatively look at the Tokina "DX" series lenses, which are designed for the aps-c sensor cameras, such as your T31.