We already can make simple ones, it's a matter of radiation shielding. They don't have to be huge expensive humanoid ones. Robots were used in the Chernobyl cleanup 25 years ago although they ended up getting fried from the radiation. I haven't done much research on the topic of what exists today regarding workarounds for electronics in radioactive environments (if someone has domain knowledge, please tell!), but I suspect we could fix that.

For some interesting history, look up "Bio-Robots" to see how the Soviet Union dealt with the disaster. Basically they sent up humans in heavy lead suits for no more than 45 seconds at a time. Run up, get three or four shovelfuls (they were clearing radioactive debris from the roof), get out.