Does this bracket exist to hold two tiles together?
I would just buy some 2"x 3" or 3"x3" aluminum angle and cut off 2" pieces and drill holes in each side.

You could get a lot of brackets from a long piece of angle and epoxy them to the tiles. Aluminum is soft enough to cut with hacksaw . 

You could use a diamond drill bit to drill the tiles and  dill holes in the angle to attach the brackets with machine bolts.   

OR 

Look at these. Playwood