Can a US citizen adopt an illegal immigrant?

Answer

No.

The person must be under the age of 14 and must be certified as an orphan or the parents must have voluntarily relinquished their rights to the child, and must have entered the US legally.

The exception is if the minor qualifies as an asylee or refugee.

Not so fast. The correct Answer is: it depends on the law of each "sovereign" state of the United States. In certain states like NY you can actually adopt an adult even if they've illegally entered the US. You can pose this question to different attorney's and I assure you that you'll get multiple answers, including "no". Always ask an attorney who specializes in family law; more specifically in adoptions.

Footnote: when the adoption is complete in NY a new Birth Certificate will be issued stating the foreign city and country of his birth, and it will clearly state "NOT A US CITIZEN".