When adopting a bird, it's not always as easy as going to the ASPCA. Some of these organizations will take in and adopt out birds, but not all. You can give them a call to inquire and even leave your contact info in the event that one turns up in their network. They may even be able to direct you to a local bird rescue.

Thorough research is required before bringing these very long-lived, very demanding, sometimes naughty, and emotionally sensitive feathered (sometimes semi-feathered) friends into our lives.

NOTE: You may have heard that a hand-fed baby birds will bond with you easier than adults. This is not always the case. 

The majority of young parrots act sweet, needy, cute, and affectionate. When they begin to mature, they may continue to be your buddy with occasional fits of sass, or they can become territorial, aggressive, and literally want to take a piece out of you. That’s why many adult birds end up re-homed multiple times over or surrendered into rescues/sanctuaries.

Parrots are social, wild animals. In their natural environment, you can see them traveling in flocks or pairs. Baby parrots are needy for their parents. When they are taken from them, they turn to humans to fill the need. When they mature, they’re often done with mom & dad, and now want a flockmate. This is where humans fill the need or cause them offense. They may or may not chill out years later.

From my experience, I learned that bird are a pandora's box of emotions. Some will hate you for months and then love you (like my Miss Cockatiel). Some will always love you (Mikey the Conure). Some will love you, then hate you, and then love you again (Elly the Conure). Some will always hate you and prefer the company of other birds (Hilda the Sassy Lovebird). 

After considering all this, if you still would like to add a bird into your family and would like to adopt, you could try to seek needy birds out via the following:

If your new bird doesn't have any medical history, make sure to get them a wellness exam with an Avian/Exotic Vet. This is even a good idea whether or not you purchased a bird from a store or breeder. 

By the time birds show signs of illness, they may have been sick for a long time, and will need to see a vet ASAP. As a survival trait, birds hide their illnesses to prevent themselves from appearing as easy prey in the wild. 
Yearly wellness exams to prevent underlying issues from becoming big problems.

I hope this has given you a little insight into the world of bird adoption and rescue.
If you'd like to learn more about the needs of companion birds, I highly recommend watching the PBS Nature Documentary Parrot Confidential or reading Of People and Parrots by Mira Tweti.