Depends on the shipper. USPS will require a cardboard box securely taped with no strings. UPS will accept a 5-gallon plastic pail with a wire handle, if the lid is secured and the handle tied down. Or, a cardboard or wood box.
It also depends on how big the anchor is. You may need to crate it, or you may be able to use stretch wrap to secure it on a large piece of corrugated cardboard, then insert that in a box and simply add packing around it to make sure it doesn't shift and break through.
Or...build a small wood crate for it, which may be the best way to make sure the galvanizing shop can just drop it back in the crate to return it to you.
If you can work with a motor
freight company both ways, you may be able to just put secure tags on the anchor and ship it "raw".