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Assuming you are US Citizen or permanent residence, US and China are both Hague adoption convention member states. Therefore you will likely to follow Hague convention process. See  travel.state.gov/content/adoptionsabroad/en/adoption-process/how-to-adopt/who-can-be-adopted.html

1.  Hague convention process

You will need to hire adoption agencies to navigate through the process.  See 
travel.state.gov/content/adoptionsabroad/en/adoption-process/how-to-adopt/hague-adoption-process.html

1.1  It bars your contact with potential adoptive children. You have to be matched, instead of your having your pick. Chinese authority pick a child for you. 

1.2. However, when the Child is a relative, you can have contact with the child or/and his/her parents and adopt directly without matching.  You still have to go through the convention process (adoption agency, home study etc), in order for the child's interest to be protected.

Relative:  travel.state.gov/content/adoptionsabroad/en/adoption-process/who-can-adopt/adopting-a-relative-for-incoming-cases.html


2. Bypass Hague, Immediate Relative process. 

If your potential child is not your relative and you want to get around Hague process, you have to become a parent to the child in the foreign country.  You need to go to China, adopt the child, and live with the child for two years in China before trying to bring him/her to USA.  Essentially you are giving up US residency to be treated as a Chinese resident.  This will bypass the Hague convention because you are not doing international adoption any more.   You became adoptive parents in China and bring the child to US as if he/she was your biological child.  

www.hooyou.com/adoption/hague-exceptions.html


See comprehensive
US state department website on international adoption here: http://travel.state.gov/content/adoptionsabroad/en.html

USCIS website regarding immigration and international adoption www.uscis.gov/adoption

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