Yes you can adopt a baby duck or even adopt an adult duck.
There are some places that have baby ducks as well as adult ducks up for adoption.
You can ask your local pet adoption center or animal shelter to see if they have a baby duck you can adopt or they may know where you can adopt a baby duck.
Another option is to place an ad on Craigslist letting people in your area know that you're looking to adopt a baby duck or even a full grown duck.
Some people may have baby ducks or even an adult duck they want to give away to a good home.
My sister adopted a full size duck using Craigslist as the guy was getting older and had no time for dealing with ducks anymore although he hated to give it away.
He was advertising free ducks and even had some baby ducks to give away as well.