The only two piece Navy anchor buttons in Albert's book are for a Chief Petty Officer and none match your button. If the back is corroded I am leaning toward it being a civilian fashion button.
Without a picture of the back, it's difficult for us to help you what you've got there.
Seeing as the back is iron and it's a two-piece button, I have to agree with ffyrffytr1 that it's a modern blazer button.