Corten steel Welding

If its less than 10mm thick and the weld is a single pass (a fillet) you can weld it with mild steel. If its MIG ER70s-6 / SG2 / G3Si1. You will get enough dilution from the plate to weatherise the weld.

If its over 10mm or if its multi-pass you need either a similar composition (nominally 1%Ni 0.5%Cu) usually classified as ER80S-G or ER80S-W alternatively you can use a 2.5% Nickel steel ER80S-Ni2

Corten A is a weathering steel that has a higher than normal copper content, this forms a rust preventative oxide on the surface that prevents "weathering" you can get a specific wire for corten but the general concensus is to treat it like s355 type material.