My dad had an affair with his brother's wife and she got pregnant and gave the baby up for adoption I know who this girl is and want to contact her but she is only sixteen Can I legally do this?

More important you should ask your self what you have to gain by contacting her, and is it in the best interest of the child. Though I don't know you or your specific circumstances, your motives seem selfish, and you haven't thought ahead to the confusion and/or disruption to the life of not just this girl, but her family. Biology does not automatically make you a welcome part of that.