Tough one!  

Obviously the best answer is the Scotty Custom Shop.

Another answer is a scotch bright sponge or steel wool. Lightly brush off the rust.  Won't solve the problem long term.  Will need to be refinished in black.

Ryan has a couple great points, the only thing I could add would be to purchase an inexpensive Scotty Cameron Oil Rag and wipe off your putter periodically.  some putters need to be wiped down after every round. 

Just a thought, Good Luck!

I did a quick internet search, but unfortunately the answer might be a nitric acid solution. In which case, you should probably just get it professionally restored by sending it to the Scotty Cameron Custom Shop.